Xpress Appendix A - Revision history

Elias at 17:28, 22 January 2012

2012-01-22T17:28:06Z

← Older revision		Revision as of 12:28, 22 January 2012
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	\|}		\|}

	~~<figtable id~~=~~"tab~~:~~callbackFunctions">~~		====Table: Callback functions.====

	{\|class="wikitable"		{\|class="wikitable"
	~~\|+<caption>Callback functions.</caption>~~
	~~\|-valign="top"~~
	!Index\|\|m-file\|\|Description		!Index\|\|m-file\|\|Description
	\|-valign="top"		\|-valign="top"
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	\|(15)\|\|vxpcb_TCM\|\|User Defined Top Cut Manager Routine		\|(15)\|\|vxpcb_TCM\|\|User Defined Top Cut Manager Routine
	\|}		\|}
	~~</figtable>~~

	====Description of Outputs====		====Description of Outputs====

Elias at 11:41, 13 December 2011

2011-12-13T11:41:27Z

← Older revision		Revision as of 06:41, 13 December 2011
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	<math>		<math>
	\begin{array}{cccccc}		\begin{array}{cccccc}
	\min\limits_{x} & ~~\multicolumn{5}{l}{~~f(x) = 0.5x^TFx + c^Tx} \\		\min\limits_{x} & f(x) = 0.5x^TFx + c^Tx \\
	s/t & x_{L} & \leq & x & \leq & x_{U} \\		s/t & x_{L} & \leq & x & \leq & x_{U} \\
	& b_{L} & \leq & Ax & \leq & b_{U} \\		& b_{L} & \leq & Ax & \leq & b_{U} \\
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	</math>		</math>

	where <math>c, x, x_{L}, x_{U}\in \~~MATHSET~~{R}^{n}</math>, <math>F\in \~~MATHSET~~{R}^{n\times n}</math>, <math>A\in \~~MATHSET~~{R}^{m\times n}</math> and <math>b_{L},b_{U}\in \~~MATHSET~~{R}^{m}</math>. The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.		where <math>c, x, x_{L}, x_{U}\in \mathbb{R}^{n}</math>, <math>F\in \mathbb{R}^{n\times n}</math>, <math>A\in \mathbb{R}^{m\times n}</math> and <math>b_{L},b_{U}\in \mathbb{R}^{m}</math>. The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

	====Calling Syntax====		====Calling Syntax====
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	<math>		<math>
	\begin{array}{cccccc}		\begin{array}{cccccc}
	\min\limits_{x} & ~~\multicolumn{5}{l}{~~f(x) = 0.5x^TFx + c^Tx } \\		\min\limits_{x} & f(x) = 0.5x^TFx + c^Tx \\
	s/t & x_{L} & \leq & x & \leq & x_{U} \\		s/t & x_{L} & \leq & x & \leq & x_{U} \\
	& b_{L} & \leq & Ax & \leq & b_{U} \\		& b_{L} & \leq & Ax & \leq & b_{U} \\
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	</math>		</math>

	where <math>c, x, x_L, x_U \in \~~MATHSET~~{R}^{n}</math>, <math>F\in \~~MATHSET~~{R}^{n\times n}</math> and <math>A\in \~~MATHSET~~{R}^{m\times n}</math>. The variables <math>b_L, b_U \in		where <math>c, x, x_L, x_U \in \mathbb{R}^{n}</math>, <math>F\in \mathbb{R}^{n\times n}</math> and <math>A\in \mathbb{R}^{m\times n}</math>. The variables <math>b_L, b_U \in
	\~~MATHSET~~{R}^{m}</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.		\mathbb{R}^{m}</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

	====Calling Syntax====		====Calling Syntax====

Elias at 12:08, 3 October 2011

2011-10-03T12:08:54Z

← Older revision		Revision as of 07:08, 3 October 2011
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	==~~Appendix A -~~ The Matlab Interface Routines - Main Routines==		{{Part Of Manual\|title=the Xpress Manual\|link=[[Xpress\|Xpress Manual]]}}
			==The Matlab Interface Routines - Main Routines==

			===xpress===

			====Purpose====
	==~~xpress==~~

	===~~Purpose~~===

	Xpress<sup>''MP''</sup> mixed-integer linear and quadratic programming (MILP, MIQP) and linear and quadratic programming (LP, QP) interface. Xpress <sup>''MP''</sup> solves problems of the form		Xpress<sup>''MP''</sup> mixed-integer linear and quadratic programming (MILP, MIQP) and linear and quadratic programming (LP, QP) interface. Xpress <sup>''MP''</sup> solves problems of the form
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	where <math>c, x, x_{L}, x_{U}\in \MATHSET{R}^{n}</math>, <math>F\in \MATHSET{R}^{n\times n}</math>, <math>A\in \MATHSET{R}^{m\times n}</math> and <math>b_{L},b_{U}\in \MATHSET{R}^{m}</math>. The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.		where <math>c, x, x_{L}, x_{U}\in \MATHSET{R}^{n}</math>, <math>F\in \MATHSET{R}^{n\times n}</math>, <math>A\in \MATHSET{R}^{m\times n}</math> and <math>b_{L},b_{U}\in \MATHSET{R}^{m}</math>. The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

	===Calling Syntax===		====Calling Syntax====

	<pre>		<pre>
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	</pre>		</pre>

	===Description of Inputs===		====Description of Inputs====

	Problem description structure. The following fields are used:		Problem description structure. The following fields are used:
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	</figtable>		</figtable>

	===Description of Outputs===		====Description of Outputs====

	The following fields are used:		The following fields are used:
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	\|}		\|}

	===Global Parameters Used===		====Global Parameters Used====

	{\|class="wikitable"		{\|class="wikitable"
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	\|}		\|}

	===Description===		====Description====

	The interface routine ''xpress'' calls Xpress ''MP'' to solve LP, QP, MILP and MIQP problems. The matrix A is transformed in xpress.m to the Xpress ''MP'' sparse matrix format. Error checking is made on the lengths of the vectors and matrices.		The interface routine ''xpress'' calls Xpress ''MP'' to solve LP, QP, MILP and MIQP problems. The matrix A is transformed in xpress.m to the Xpress ''MP'' sparse matrix format. Error checking is made on the lengths of the vectors and matrices.

	==xpressTL==		===xpressTL===

	===Purpose===		====Purpose====

	The TOMLAB ''/''Xpress MILP, MIQP, LP and QP Interface. It solves linear programming (LP), quadratic programming (QP), mixed integer linear programming (MILP) and mixed integer quadratic programming problems (MIQP). ''xpressTL ''solves problems of the form		The TOMLAB ''/''Xpress MILP, MIQP, LP and QP Interface. It solves linear programming (LP), quadratic programming (QP), mixed integer linear programming (MILP) and mixed integer quadratic programming problems (MIQP). ''xpressTL ''solves problems of the form
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	\MATHSET{R}^{m}</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.		\MATHSET{R}^{m}</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

	===Calling Syntax===		====Calling Syntax====

	<pre>		<pre>
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	</pre>		</pre>

	===Description of Inputs===		====Description of Inputs====

	''Prob'', the problem structure. The following fields are used:		''Prob'', the problem structure. The following fields are used:
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	\|}		\|}

	===Description of Outputs===		====Description of Outputs====

	''Result ''structure. The following fields are used:		''Result ''structure. The following fields are used:
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	\|}		\|}

	===Global Parameters Used===		====Global Parameters Used====

	{\|class="wikitable"		{\|class="wikitable"
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	\|}		\|}

	===Description===		====Description====

	The TOMLAB Xpress''M P ''MILP, MIQP, QP and LP interface calls the interface routine ''xpress.m''. Values ''> ''1020 and ''I nf ''values are set to 1020 , and the opposite for negative numbers. An empty objective coefficient ''c''-vector is set to the zero-vector.		The TOMLAB Xpress''M P ''MILP, MIQP, QP and LP interface calls the interface routine ''xpress.m''. Values ''> ''1020 and ''I nf ''values are set to 1020 , and the opposite for negative numbers. An empty objective coefficient ''c''-vector is set to the zero-vector.

	===Examples===		====Examples====

	See ''mip prob''		See ''mip prob''

	===M-files Used===		====M-files Used====

	''xpress.m'', ''mipRun.m''		''xpress.m'', ''mipRun.m''

	===See Also===		====See Also====

	''mipSolve''		''mipSolve''

Elias at 11:59, 3 October 2011

2011-10-03T11:59:14Z

Show changes

Elias: Created page with "==Appendix A - The Matlab Interface Routines - Main Routines== ==xpress== ===Purpose=== Xpress^''MP'' mixed-integer linear and quadratic programming (MILP, MIQP)..."

2011-09-28T08:31:27Z

Created page with "==Appendix A - The Matlab Interface Routines - Main Routines== ==xpress== ===Purpose=== Xpress''MP'' mixed-integer linear and quadratic programming (MILP, MIQP)..."

New page

==Appendix A - The Matlab Interface Routines - Main Routines==

==xpress==

===Purpose===

Xpress''MP'' mixed-integer linear and quadratic programming (MILP, MIQP) and linear and quadratic programming (LP, QP) interface. Xpress ''MP'' solves problems of the form

<math>
\begin{array}{cccccc}
\min\limits_{x} & \multicolumn{5}{l}{f(x) = 0.5*x^T*F*x + c^T*x} \\
s/t & x_{L} & \leq & x & \leq & x_{U} \\
& b_{L} & \leq & Ax & \leq & b_{U} \\
& & & x_i \mathrm{\ \ integer} & & i \in I \\
\end{array}
</math>

where <math>c, x, x_{L}, x_{U}\in \MATHSET{R}^{n}</math>, <math>F\in \MATHSET{R}^{n\times n}</math>, <math>A\in \MATHSET{R}^{m\times n}</math> and <math>b_{L},b_{U}\in \MATHSET{R}^{m}</math>. The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

===Calling Syntax===

<pre>
[x, slack, v, rc, f k, ninf, sinf, Inform, basis, lpiter, glnodes] = xpress(c, A, x L, x U, b L, b U, xpcontrol, call- back, PriLev, Prob, IntVars, PI, SC, SI, sos1, sos2, F, LogFile, SaveFile, SaveMode, iisRequest, iisFile, saRequest);
</pre>

===Description of Inputs===

Problem description structure. The following fields are used:

{|class="wikitable"
|''c''||Linear objective function cost coefficients, vector ''n × ''1.
|-valign="top"
|''F''||Square dense or sparse matrix. Empty if non-quadratic problem.
|-valign="top"
|''A''||Linear constraint matrix for linear constraints, dense or sparse matrix ''m × n''.
|-valign="top"
|''x_L''||Lower bounds on design parameters ''x''. If empty assumed as zero.
|-valign="top"
|''x_U''||Upper bounds on design parameters ''x''.
|-valign="top"
|''b_L''||Lower bounds on the linear constraints.
|-valign="top"
|||'''The following parameters are optional:'''
|-valign="top"
|''b_U''||Upper bounds on the linear constraints. If empty, then ''bU ''= ''bL ''assumed.
|-valign="top"
|''xpcontrol''||Structure, where the fields are set to the Xpress''M P ''control parameters that the user wants to specify values for. The control parameters are listed in Section 7 in the Xpress-Optimizer Reference Manual [1]. The prefix XPRS is not used.
|-valign="top"
|''callback''||Logical vector defining which callbacks to use in Xpress''M P ''. If the ''i''th entry of the logical vector ''callback ''is set, the corresponding callback is defined. See Section 5.3 in [1]. The callback calls the m-file specified in Table 9 below. The user may edit this file, or make a new copy, which is put in a directory that is searched before the ''xpress ''directory in the Matlab path.
|-valign="top"
|''PriLev''||Printing level in the ''xpress m''-file and the Xpress ''MP'' C-interface.

= 0 Silent

= 1 Summary information

= 2 More detailed information
|-valign="top"
|''Prob''||A structure. If TOMLAB calls ''xpress'', then ''Prob'' is the standard TOMLAB problem structure, otherwise the user optionally may set: ''P rob.P ''= ''P roblemN umber''; , where ProblemNumber is some integer. If any callback is defined then problem arrays are set as fields in ''Prob'', and the ''Prob ''structure is always passed to the callback routines as the last parameter. The defined fields are ''Prob.c'', ''Prob.x L'', ''Prob.x U'', ''Prob.A'', ''Prob.b L'', ''Prob.b U ''and ''Prob.QP.F''. If the input structure is empty ([ ]), then ''P rob.P ''= 1 is set. If ''Prob.MIP.KNAPSACK = 1 ''and ''callback''(9) == 1, then the simple heuristic in ''xpcb GL ''is used. If callback(9) is set, and ''Prob.MIP.KNAPSACK'', or ''Prob.MIP ''is undefined, ''xpress ''is setting ''Prob.MIP.KNAPSACK = 0'', to avoid the call to the heuristic.
|-valign="top"
|''IntVars''||Defines which variables are integers, of the general type ''I ''or binary ''B''. Variable indices should be in the range [1,...,n]. If ''I ntV ars ''is a logical vector then all variables ''i ''where ''I ntV ars''(''i'') ''> ''0 are defined to be integers. If ''I ntV ars ''is determined to be a vector of indices then ''x''(''I ntV ars'') are defined as integers. If the input is empty ([ ]), then no integers of type I or B are defined. The interface routine ''xpress ''checks which of the integer variables have lower bound ''xL ''= 0 and upper bound ''xU ''= 1, i.e. are binary 0/1 variables.
|-valign="top"
|''PI''||Integer variables of type ''Partially Integer ''(PI), i.e. takes an integer value up to a specified limit, and any real value above that limit. PI must be a structure array where:

''PI.var'' is a vector of variable indices in the range [1'', ..., n''].

''PI.lim'' is a vector of limit values for each of the variables specified in PI.var, i.e. for variable ''i'', that is the PI variable with index ''j ''in ''P I .var'', then ''x''(''i'') takes integer values in [''xL ''(''i'')'', P I .lim''(''j'')] and continuous values in [''P I .lim''(''j'')'', xU ''(''i'')].
|-valign="top"
|''SC''||A vector with indices for the integer variables of type ''Semi-continuous ''(SC), i.e. that takes either the value 0 or a real value in the range [''xL ''(''i'')'', xU ''(''i'')], assuming for some ''j'', that ''i ''= ''SC ''(''j''), where ''i ''is an variable number in the range [1'', ..., n''].
|-valign="top"
|''SI''||A vector with indices for the integer variables of type ''Semi-integer ''(SI), i.e. that takes either the value 0 or an integer value in the range [''xL ''(''i'')'', xU ''(''i'')], assuming for some ''j'', that ''i ''= ''SI ''(''j''), where ''i ''is an variable number in the range [1'', ..., n''].
|-valign="top"
|''sos1''||A structure defining the ''Special Ordered Sets of Type One ''(sos1). Assume there are ''k ''sets of type sos1, then ''sos''1(''k'')''.var ''is a vector of indices for variables of type sos1 in set ''k''. ''sos''1(''k'')''.row ''is the row number for the reference row identifying the ordering information for the sos1 set, i.e. A(sos1(k).row,sos1(k).var) identifies this information. As ordering information, also the objective function coefficients ''c ''could be used. Then as row number, 0 is instead given in ''sos''1(''k'')''.row''.
|-valign="top"
|''sos2''||A structure defining the ''Special Ordered Sets of Type Two ''(sos2). Specified exactly as sos1 sets, see ''sos''1 input variable description.
|-valign="top"
|''LogFile''||File to write Xpress-MP log output to. Default is empty " in which case nothing is written.

Please note that Xpress-MP appends it's output to the log file.
|-valign="top"
|''SaveFile''||Filename for writing the problem prior to calling the Xpress-MP solver. If empty, no file is written. The type of output is determined by the SaveMode parameter. Xpress-MP will always add an extension to the filename given here. The extension depends on the SaveMode chosen, see below.
|-valign="top"
|''SaveMode''||Character string with any combination of the following character flags:

p - full precision of numerical values. o - one element per line.

n - scaled.

s - scrambled vector names. l - output in LP format.

The extension added to the SaveFile name is .mat, unless the 'l' flag is used in which case the extension is .lp.
|-valign="top"
|''iisRequest''||Flag indicating whether to compute an IIS and return it to MATLAB. This option can only be set for an LP problem. If an IIS is found, XPRESS automatically changes the problem to make it feasible and reoptimizes it.

= 0, Don't return IIS to MATLAB (default).

= 1, Compute IIS and return it to MATLAB if an LP problem has been proven infeasible. The IIS is returned through the output parameter 'iis'.
|-valign="top"
|''iisFile''||Flag indicating whether to write a file describing the IIS set or not. If is set to 1, a file: LPprob.iis will be written. Otherwise, no file is written..
|-valign="top"
|''saRequest''||Structure telling whether and how you want XPRESS to perform a sensitivity analysis (SA).

You can complete an SA on the objective function and right hand side vector. The saRequest structure contains two sub structures:

.obj and .rhs

They have one field each:

.index

In case of .obj.index, .index contains the indices of the columns whose objective function coefficients sensitivity ranges are required.

In case of .rhs.index, .index contains the indices of the rows whose RHS coefficients sensitivity ranges are required.

In both cases, the .index array has to be sorted, ascending.

To get an SA of objective function on the four variables 120 to 123 (included) and variable

6 the saRequest structure would look like this:

saRequest.obj.index = [6 120 121 122 123];

The result is returned through the output parameter 'sa'.
|}

<figtable id="tab:callbackFunctions">
{|class="wikitable"
|+<caption>Callback functions.</caption>
|-valign="top"
!Index||m-file||Description
|(1)||xpcb_USN||User Select Node Callback
|-valign="top"
|(2)||xpcb UPN||User Preprocess Node Callback
|-valign="top"
|(3)||xpcb UON||User Optimal Node Callback
|-valign="top"
|(4)||xpcb UIN||User Infeasible Node Callback
|-valign="top"
|(5)||xpcb UIS||User Integer Solution Callback
|-valign="top"
|(6)||xpcb UCN||User Node Cut-off Callback
|-valign="top"
|(7)||xpcb UCB||User Choose Branching Variable Callback
|-valign="top"
|(8)||xpcb IL||Simplex Log Callback
|-valign="top"
|(9)||xpcb GL||Global Log Callback
|-valign="top"
|(10)||xpcb BL||Barrier Log Callback
|-valign="top"
|(11)||xpcb UOP||User Output Callback
|-valign="top"
|(12)||xpcb CMI||User Defined Cut Manager Init Routine
|-valign="top"
|(13)||xpcb CMS||User Defined Cut Manager Termination Routine
|-valign="top"
|(14)||xpcb CM||User Defined Cut Manager Routine
|-valign="top"
|(15)vxpcb TCM||User Defined Top Cut Manager Routine
|}
</figtable>

===Description of Outputs===

The following fields are used:

{|class="wikitable"
!Output||Description
|-valign="top"
|''x''||Solution vector ''x ''with decision variable values (''n × ''1 vector).
|-valign="top"
|''slack''||Slack variables (''m × ''1 vector).
|-valign="top"
|''v''||Lagrangian multipliers (dual solution vector) (''m × ''1 vector).
|-valign="top"
|''rc ''||Reduced costs. Lagrangian multipliers for simple bounds on ''x''.
|-valign="top"
|''f_k ''||Objective function value ''f ''(''x'') = ''cT * x ''at optimum.
|-valign="top"
|''ninf ''||Number of infeasibilities.
|-valign="top"
|''sinf ''||Sum of infeasibilities.
|-valign="top"
|''Inform ''||Result of Xpress''M P ''run:

{|class="wikitable"
|0||Optimal solution found.
|-valign="top"
|2||Unbounded solution.
|-valign="top"
|4||Infeasible problem.
|-valign="top"
|5||Some error occurred.
|}

See the Xpress''MP'' problem attributes XPRS LPSTATUS (for LP and QP) and XPRS MIPSTATUS (for MILP and MIQP) for more exact information. They are available in the global variable ''xpProblemAttrib''.
|-valign="top"
|''basis ''||Basis status of constraints and variables, (''m ''+ ''n × ''1 vector).
|-valign="top"
|''lpiter''||Number of simplex iterations.
|-valign="top"
|''glnodes''||Number of nodes visited.
|-valign="top"
|''iis''||Structure containing IIS information (niis x 1). niis is the number of IISs found (see MAXIIS parameter). The fields:
|-valign="top"
|''iisStatus''||Status flag. (Only set in the first element of the iis array.) Possible values:

2 = IIS was written to file LPprob.iis.

1 = IIS was obtained.

-1 = Problem was infeasible but no IIS found.

-2 = Problem was not infeasible.
|-valign="top"
|''iisMessage''||Error message on error. (Only set in the first element of the iis array.)
|-valign="top"
|''colind''||The column indices of the IIS set.
|-valign="top"
|''rowind ''||The row indices of the IIS set.
|-valign="top"
|''sa''||Structure with information about the requested SA, if requested. The fields:
|-valign="top"
|''obj''||Ranges for the variables in the objective function.
|-valign="top"
|''rhs''||Ranges for the right hand side values.
|-valign="top"
|colspan="2"||These fields are structures themselves. All four structures have identical field names:
|-valign="top"
|''status''||Status of the SA operation. Possible values:

1 = Successful.

0 = SA not requested.

-1 = Error: MIP problem was presolved.
|-valign="top"
|''lower ''||The lower range.
|-valign="top"
|''upper ''||The upper range.
|}

===Global Parameters Used===

{|class="wikitable"
!Parameter||Description
|-valign="top"
|''xpControlVariables''||Structure with all Xpress''MP'' control variables listed in Section 7 in the Xpress-Optimizer Reference Manual [1]. Available with fresh variables in each callback, and after the optimization.
|-valign="top"
|''xpProblemAttrib''||Structure with all Xpress ''MP'' problem attributes listed in Section 8 in the Xpress-Optimizer Reference Manual [1]. Available with fresh values in each callback, and after the optimization.
|}

===Description===

The interface routine ''xpress'' calls Xpress ''MP'' to solve LP, QP, MILP and MIQP problems. The matrix A is transformed in xpress.m to the Xpress ''MP'' sparse matrix format. Error checking is made on the lengths of the vectors and matrices.

==xpressTL==

===Purpose===

The TOMLAB ''/''Xpress MILP, MIQP, LP and QP Interface. It solves linear programming (LP), quadratic programming (QP), mixed integer linear programming (MILP) and mixed integer quadratic programming problems (MIQP). ''xpressTL ''solves problems of the form

<math>
\begin{array}{cccccc}
\min\limits_{x} & \multicolumn{5}{l}{f(x) = 0.5*x^T*F*x + c^T*x } \\
s/t & x_{L} & \leq & x & \leq & x_{U} \\
& b_{L} & \leq & Ax & \leq & b_{U} \\
& & & x_i \mathrm{\ \ integer} & & i \in I \\
\end{array}
</math>

where <math>c, x, x_L, x_U \in \MATHSET{R}^{n}</math>, <math>F\in \MATHSET{R}^{n\times n}</math> and <math>A\in \MATHSET{R}^{m\times n}</math>. The variables <math>b_L, b_U \in
\MATHSET{R}^{m}</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

===Calling Syntax===

<pre>
Prob = ProbCheck(Prob, 'xpress');
Result = xpressTL(Prob);
</pre>

===Description of Inputs===

''Prob'', the problem structure. The following fields are used:

{|class="wikitable"
!Field||Description
|-valign="top"
|''QP.c''||Linear objective function cost coefficients, vector ''n × ''1.
|-valign="top"
|''QP.F''||Square ''n × n ''dense or sparse matrix. Empty if non-quadratic problem.
|-valign="top"
|''A''||Linear constraint matrix for linear constraints, dense or sparse ''m × n ''matrix.
|-valign="top"
|''x_L''||Lower bounds on design parameters ''x''. If empty assumed to be ''-I nf ''.
|-valign="top"
|''x_U''||Upper bounds on design parameters ''x''. If empty assumed to be ''I nf ''.
|-valign="top"
|''b_L''||Lower bounds on the linear constraints.
|-valign="top"
|''b_U''||Upper bounds on the linear constraints.
|-valign="top"
|''PriLev''||Printing level in the ''xpress m''-file and the Xpress''M P ''C-interface.

= 0 Silent

= 1 Summary information

= 2 More detailed information
|-valign="top"
|''MIP.IntVars''||Defines which variables are integers, of the general type ''I ''or binary ''B''. Variable indices should be in the range [1,...,n]. If ''I ntV ars ''is a logical vector then all variables ''i ''where ''I ntV ars''(''i'') ''> ''0 are defined to be integers. If ''I ntV ars ''is determined to be a vector of indices then ''x''(''I ntV ars'') are defined as integers. If the input is empty ([ ]), then no integers of type I or B are defined. The interface routine ''xpress ''checks which of the integer variables have lower bound ''xL ''= 0 and upper bound ''xU ''= 1, i.e. are binary 0/1 variables.
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|''MIP.PI''||Integer variables of type ''Partially Integer ''(PI), i.e. takes an integer value up to a specified limit, and any real value above that limit. PI must be a structure array where:

''PI.var ''is a vector of variable indices in the range [1'', ..., n''].
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|''PI.lim''||is a vector of limit values for each of the variables specified in PI.var, i.e. for variable ''i'', that is the PI variable with index ''j''in ''P I .var'', then ''x''(''i'') takes integer values in [''xL ''(''i'')'', P I .lim''(''j'')] and continuous values in [''P I .lim''(''j'')'', xU ''(''i'')].
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|''MIP.SC''||A vector with indices for the integer variables of type ''Semi-continuous ''(SC), i.e. that takes either the value 0 or a real value in the range [''xL ''(''i'')'', xU ''(''i'')], assuming for some ''j'', that ''i ''= ''SC ''(''j''), where ''i ''is an variable number in the range [1'', ..., n''].
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|''MIP.SI''||A vector with indices for the integer variables of type ''Semi-integer ''(SI), i.e. that takes either the value 0 or an integer value in the range [''xL ''(''i'')'', xU ''(''i'')], assuming for some ''j'', that ''i ''= ''SI ''(''j''), where ''i ''is an variable number in the range [1'', ..., n''].
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|''MIP.sos1''||A structure defining the ''Special Ordered Sets of Type One ''(sos1). Assume there are ''k ''sets of type sos1, then ''sos''1(''k'')''.var ''is a vector of indices for variables of type sos1 in set ''k''. ''sos''1(''k'')''.row ''is the row number for the reference row identifying the ordering information for the sos1 set, i.e. A(sos1(k).row,sos1(k).var) identifies this information. As ordering information, also the objective function coefficients ''c ''could be used. Then as row number, 0 is instead given in ''sos''1(''k'')''.row''.
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|''MIP.sos2''||A structure defining the ''Special Ordered Sets of Type Two ''(sos2). Specified exactly as sos1 sets, see ''M I P.sos''1 input variable description.
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|''MIP.KNAPSACK''||True if a knapsack problem is to be solved and a knapsack heuristic is to be used. Also ''MIP.callback''(9) = 1 must be set if the heuristic is to be executed.
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|''MIP.xpcontrol''||Structure, where the fields are set to the Xpress''M P ''control parameters that the user wants to specify values for. The control parameters are listed in Section 7 in the Xpress-Optimizer Reference Manual [1]. The prefix XPRS is not used.
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|''MIP.callback''||Logical vector defining which callbacks to use in Xpress''M P ''. If the ''i''th entry of the logical vector ''callback ''is set, the corresponding callback is defined. See Section 5.3 in [1]. The callback calls the m-file specified in the Table 12 below. The user may edit this file, or make a new copy, which is put in a directory that is searched before the ''xpress ''directory in the Matlab path.
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|''optParam''||Structure with special fields for optimization parameters

Fields used are: ''MaxIter ''- Maximal number of iterations or node visits.
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|''XPRESS.LogFile''||File to write Xpress-MP log output to. Default is empty " in which case nothing is written.

Please note that Xpress-MP appends it's output to the log file.
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|''XPRESS.SaveFile''||Filename for writing the problem prior to calling the Xpress-MP solver. If empty, no file is written. The type of output is determined by the SaveMode parameter. Xpress-MP will always add an extension to the filename given here. The extension depends on the SaveMode chosen, see below.
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|''XPRESS.SaveMode''||Character string with any combination of the following character flags:

p - full precision of numerical values. o - one element per line.

n - scaled.

s - scrambled vector names. l - output in LP format.

The extension added to the SaveFile name is .mat, unless the 'l' flag is used in which case the extension is .lp.
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|''iis''||Flag indicating whether to compute an IIS and return it to MATLAB. This option can only be set for an LP problem. If an IIS is found, XPRESS automatically changes the problem to make it feasible and reoptimizes it.

= 0, Don't return IIS to MATLAB (default).

= 1, Compute IIS and return it to MATLAB if an LP problem has been proven infeasible. The IIS is returned through the output parameter 'iis'.
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|''iisFile''||Flag indicating whether to write a file describing the IIS set or not. If is set to 1, a file: LPprob.iis will be written. Otherwise, no file is written.
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|''sa''||Structure telling whether and how you want XPRESS to perform a sensitivity analysis (SA).

You can complete an SA on the objective function and right hand side vector. The saRequest structure contains two sub structures:

.obj and .rhs

They have one field each:

.index

In case of .obj.index, .index contains the indices of the columns whose objective function coefficients sensitivity ranges are required.

In case of .rhs.index, .index contains the indices of the rows whose RHS coefficients sensitivity ranges are required.

In both cases, the .index array has to be sorted, ascending.

To get an SA of objective function on the four variables 120 to 123 (included) and variable

6 the saRequest structure would look like this:

saRequest.obj.index = [6 120 121 122 123];

The result is returned through the output parameter 'sa'.

{|class="wikitable"
|+<caption>Callback functions.</caption>
!Index||m-file||Description
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|(1)||xpcb USN||User Select Node Callback
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|(2)||xpcb UPN||User Preprocess Node Callback
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|(3)||xpcb UON||User Optimal Node Callback
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|(4)||xpcb UIN||User Infeasible Node Callback
|-valign="top"
|(5)||xpcb UIS||User Integer Solution Callback
|-valign="top"
|(6)||xpcb UCN||User Node Cut-off Callback
|-valign="top"
|(7)||xpcb UCB||User Choose Branching Variable Callback
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|(8)||xpcb IL||Simplex Log Callback
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|(9)||xpcb GL||Global Log Callback
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|(10)||xpcb BL||Barrier Log Callback
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|(11)||xpcb UOP||User Output Callback
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|(12)||xpcb CMI||User Defined Cut Manager Init Routine
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|(13)||xpcb CMS||User Defined Cut Manager Termination Routine
|-valign="top"
|(14)||xpcb CM||User Defined Cut Manager Routine
|-valign="top"
|(15)||xpcb TCM||User Defined Top Cut Manager Routine
|}

===Description of Outputs===

''Result ''structure. The following fields are used:

!Output||Description
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|''Iter''||Number of iterations, or nodes visited.
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|''ExitFlag''||0: OK.

1: Maximal number of iterations reached.

2: Unbounded feasible region.

4: No feasible point found.

5: Error of some kind.
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|''Inform''||If a MIP problem the control variable XPRS MIPSTATUS (xpControlVari- ables.MIPSTATUS) else XPRS LPSTATUS (xpControlVariables.LPSTATUS).
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|''x_0''||Initial starting point not known, set as empty.
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|''QP.B''||Optimal active set, basis vector, in TOMLAB QP standard.

''B''(''i'') = 1: Include variable ''x''(''i'') is in basic set.

''B''(''i'') = 0: Variable ''x''(''i'') is set on its lower bound.

''B''(''i'') = ''-''1: Variable ''x''(''i'') is set on its upper bound.
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|''f_k''||Function value at optimum, ''f ''(''xk '').
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|''g_k''||Gradient value at optimum, ''c ''or ''c ''+ ''F * x''.
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|''x_k''||Optimal solution vector ''xk ''.
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|''v_k''||Lagrangian multipliers (for bounds and dual solution vector). Set as ''vk ''= [''rc''; ''v''], where ''rc'' is the ''n''-vector of reduced costs and ''v ''holds the ''m ''dual variables.
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''xState''||State of each variable.

0 = nonbasic (on x L), 1 = nonbasic (on x U), 2 = superbasic (between bounds), 3 = basic

(between bounds)
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|''bState''||State of each constraint.

0 = nonbasic (on b L), 1 = nonbasic (on b U), 2 = superbasic (between bounds), 3 = basic

(between bounds)

|''Solver''||Solver used - Xpress''M P ''.
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|''SolverAlgorithm''||Solver algorithm used.
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|''FuncEv''||Number of function evaluations. Set to ''Iter''. ''GradEv ''Number of gradient evaluations. Set to ''Iter''. ''ConstrEv ''Number of constraint evaluations. Set to ''Iter''. ''Prob ''Problem structure used.
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|''MIP.ninf''||Number of infeasibilities.
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|''MIP.sinf''||Sum of infeasibilities.
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|''MIP.slack''||Slack variables (''m × ''1 vector).
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|''MIP.lpiter''||Number of LP iterations.
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|''MIP.glnodes''||Number of nodes visited.
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|''MIP.basis''||Basis status of constraints and variables (''m ''+ ''n × ''1 vector) in the Xpress''MP'' format, fields xState and bState has the same information in the Tomlab format.
|-valign="top"
|''MIP.xpControlVariables''||Structure with all Xpress''M P ''control variables listed in Section 7 in the Xpress-Optimizer eference Manual [1].
|-valign="top"
|''MIP.xpProblemAttrib''||Structure with all Xpress''M P ''problem attributes listed in Section 8 in the Xpress-Optimizer Reference Manual [1].
|-valign="top"
|''XPRESS.iis''||Structure containing IIS information (niis x 1). niis is the number of IISs found (see MAXIIS parameter). The fields:
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|''iisStatus''||Status flag. (Only set in the first element of the iis array.) Possible values:

2 = IIS was written to file LPprob.iis.

1 = IIS was obtained.

-1 = Problem was infeasible but no IIS found.

-2 = Problem was not infeasible.
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|''iisMessage ''||Error message on error. (Only set in the first element of the iis array.)
|-valign="top"
|''colind ''||The column indices of the IIS set.
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|''rowind ''||The row indices of the IIS set.
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|''XPRESS.sa ''||Structure with information about the requested SA, if requested. The fields:
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|''obj ''||Ranges for the variables in the objective function.
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|''rhs ''||Ranges for the right hand side values.
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|colspan="2"|These fields are structures themselves. All four structures have identical field names:
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|''status''||Status of the SA operation. Possible values:

1 = Successful.

0 = SA not requested.

-1 = Error: MIP problem was presolved.
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|''lower''||The lower range.
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|''upper''||The upper range.
|}

===Global Parameters Used===

{|class="wikitable"
|''xpControlVariables''||Structure with all Xpress''M P ''control variables listed in Section 7 in the Xpress- Optimizer Reference Manual [1]. Available with fresh variables in each callback, and after the optimization.
|-valign="top"
|''xpProblemAttrib''||Structure with all Xpress''M P ''problem attributes listed in Section 8 in the Xpress- Optimizer Reference Manual [1]. Available with fresh variables in each callback, and after the optimization.
|}

===Description===

The TOMLAB Xpress''M P ''MILP, MIQP, QP and LP interface calls the interface routine ''xpress.m''. Values ''> ''1020 and ''I nf ''values are set to 1020 , and the opposite for negative numbers. An empty objective coefficient ''c''-vector is set to the zero-vector.

===Examples===

See ''mip prob''

===M-files Used===

''xpress.m'', ''mipRun.m''

===See Also===

''mipSolve''

Xpress Appendix A - Revision history

Elias at 17:28, 22 January 2012

Elias at 11:41, 13 December 2011

Elias at 12:08, 3 October 2011

Elias at 11:59, 3 October 2011

Elias: Created page with "==Appendix A - The Matlab Interface Routines - Main Routines== ==xpress== ===Purpose=== Xpress''MP'' mixed-integer linear and quadratic programming (MILP, MIQP)..."

Elias: Created page with "==Appendix A - The Matlab Interface Routines - Main Routines== ==xpress== ===Purpose=== Xpress^''MP'' mixed-integer linear and quadratic programming (MILP, MIQP)..."