Elias at 15:17, 9 December 2011

2011-12-09T15:17:31Z

← Older revision		Revision as of 11:17, 9 December 2011
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	</math>		</math>

	where <math>x \in \~~MATHSET~~{R}^n</math>, <math>y \in \~~MATHSET~~{R}^M</math>, <math>H \in		where <math>x \in \mathbb{R}^n</math>, <math>y \in \mathbb{R}^M</math>, <math>H \in
	\~~MATHSET~~{R}^{M \times n}</math>, <math>A \in \~~MATHSET~~{R}^{m_1 \times n}</math>,		\mathbb{R}^{M \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math>,
	<math>b_L,b_U \in \~~MATHSET~~{R}^{n+m_1}</math>.		<math>b_L,b_U \in \mathbb{R}^{n+m_1}</math>.

	Dependent on the input of H, y, c and Upper, any of the following ten problems are solved. If m == length(y) ''>'' 0, then a LS problem is assumed Upper is ''> ''0 ==''> ''H is upper trapezodial.		Dependent on the input of H, y, c and Upper, any of the following ten problems are solved. If m == length(y) ''>'' 0, then a LS problem is assumed Upper is ''> ''0 ==''> ''H is upper trapezodial.
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	</math>		</math>

	where <math>x, x_L, x_U \in \~~MATHSET~~{R}^n</math>, <math>d \in \~~MATHSET~~{R}^M</math>, <math>C		where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>d \in \mathbb{R}^M</math>, <math>C
	\in \~~MATHSET~~{R}^{M \times n}</math>, <math>A \in \~~MATHSET~~{R}^{m_1 \times n}</math>,		\in \mathbb{R}^{M \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math>,
	<math>b_L,b_U \in \~~MATHSET~~{R}^{m_1}</math>.		<math>b_L,b_U \in \mathbb{R}^{m_1}</math>.

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

Elias at 08:57, 23 August 2011

2011-08-23T08:57:31Z

← Older revision		Revision as of 04:57, 23 August 2011
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	A direct solver call is not recommended unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to [[#Using TOMLAB]] for information on how to use LSSOL with TOMLAB.		A direct solver call is not recommended unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to [[#Using TOMLAB]] for information on how to use LSSOL with TOMLAB.

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

	''lssol ''solves least squares optimization problems defined as		''lssol ''solves least squares optimization problems defined as
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	\|}		\|}

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

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

Elias at 08:41, 23 August 2011

2011-08-23T08:41:22Z

@@ Line 3: / Line 3: @@
 ==Direct  Solver Call==
-A direct solver call is not recommended  unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to Section 3.6.2 for information on how to use LSSOL with TOMLAB.
+A direct solver call is not recommended  unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to [[#Using TOMLAB]] for information on how to use LSSOL with TOMLAB.
 ==Purpose==
@@ Line 9: / Line 9: @@
 ''lssol ''solves least squares optimization problems defined as
 Dependent on the input of H, y, c and Upper, any of the following ten problems are solved. If m == length(y) ''>'' 0, then a LS problem is assumed Upper is ''> ''0 ==''> ''H is upper trapezodial.
@@ Line 145: / Line 160: @@
 ===Calling  Syntax===

Elias: Created page with "{{Part Of Manual|title=the SOL Manual|link=SOL}} ==Direct Solver Call== A direct solver call is not recommended unless the user is 100 % sure that no other solvers wi..."

2011-08-22T16:18:11Z

Created page with "{{Part Of Manual|title=the SOL Manual|link=SOL}} ==Direct Solver Call== A direct solver call is not recommended unless the user is 100 % sure that no other solvers wi..."

New page

{{Part Of Manual|title=the SOL Manual|link=[[SOL|SOL]]}}

==Direct Solver Call==

A direct solver call is not recommended unless the user is 100 % sure that no other solvers will be used for the problem. Please refer to Section 3.6.2 for information on how to use LSSOL with TOMLAB.

==Purpose==

''lssol ''solves least squares optimization problems defined as

Dependent on the input of H, y, c and Upper, any of the following ten problems are solved. If m == length(y) ''>'' 0, then a LS problem is assumed Upper is ''> ''0 ==''> ''H is upper trapezodial.

{|class="wikitable"
|+<caption>Problems solved by LSSOL.</caption>
!H
!y
!c
!Upper
!Description!!
|-valign="top"
|empty||empty||empty||-||Feasible point problem||(FP)
|-valign="top"
|empty||empty||n x 1||-||Linear programming problem||(LP)
|-valign="top"
|n x n||empty||empty||0||Quadratic programming problem||(QP1)
|-valign="top"
|n x n||empty||n x 1||0||Quadratic programming problem||(QP2)
|-valign="top"
|n x n||empty||empty||1||Quadratic programming problem||(QP3)
|-valign="top"
|n x n||empty||n x 1||1||Quadratic programming problem||(QP4)
|-valign="top"
|m x n||m||empty||0||Least squares problem||(LS1)
|-valign="top"
|m x n||m||n x 1||0||Least squares problem||(LS2)
|-valign="top"
|m x n||m||empty||1||Least squares problem||(LS3)
|-valign="top"
|m x n||m||n x 1||1||Least squares problem||(LS4)
|}

===Calling Syntax===

<pre>
[x, Inform, iState, cLamda, Iter, fObj, r, kx] = lssol(A, bl, bu, c, x, optPar, H, y,
Warm, iState, Upper, kx, SpecsFile, PrintFile, SummFile, PriLev, ProbName );
</pre>

===Description of Inputs===

{|class="wikitable"
!colspan="2"|The following fields are used:
|-valign="top"
|''A ''||Constraint matrix, nclin x n (DENSE).
|-valign="top"
|''bl ''||Lower bounds on (x,Ax), nclin+n x 1 vector (DENSE).
|-valign="top"
|''bu ''||Upper bounds on (x,Ax), nclin+n x 1 vector (DENSE).
|-valign="top"
|''c''||Linear objective function cost coeffs, n x 1 (DENSE). If isempty(c), setting c(1:n)=0;.
|-valign="top"
|''x ''||Initial estimate of solution vector x. If isempty(x), x(1:n)=0.
|-valign="top"
|''optPar ''||Vector with optimization parameters overriding defaults and the optionally specified SPECS file. If length(optPar) ¡ 62, lssol sets the rest of the values to missing value (-999).
|-valign="top"
|''H ''||Matrix H in quadratic part of objective function (DENSE). H is either empty (FP, LP), or quadratic n x n (QP), or m x n (LS).
|-valign="top"
|''y ''||Data vector of length m for LS problem, otherwise empty.
|-valign="top"
|''Warm ''||If Warm ''> ''0, then warm start, otherwise cold Start. Default 0. If warm start, then x and iState must be set properly. Normally the values from last call to lssol are used.
|-valign="top"
|''iState ''||Working set (if Warm start) (nclin+m) x 1 (DENSE). If length(iState) ¡nclin+m, setting iState(1:n+m)=0 & Warm=0.

''iState(i)=0: ''Corresponding constraint not in the initial working set.

''iState(i)=1: ''Inequality constraint at its lower bound in working set.

''iState(i)=2: ''Inequality constraint at its upper bound in working set.

''iState(i)=3: ''Equality constraint in the initial working set, bl(i)==bu(i).
|-valign="top"
|''Upper ''||If ''> ''0, then H must be an upper-trapezoidal matrix.
|-valign="top"
|''kx ''||Order of the n columns in A for the QP3, QP4, LS3 or LS4 problem.
|-valign="top"
|''SpecsFile ''||Name of the OPTIONS File, see TOMLAB Guide.
|-valign="top"
|''PrintFile ''||Name of the Print file. Name includes the path, maximal number of characters = 500.
|-valign="top"
|''SummFile ''||Name of the Summary file. Name includes the path, maximal number of characters = 500.
|-valign="top"
|''PriLev ''||Print level in the lssol MEX-interface..

= 0 Silent

= 10 Dimensions are printed

if isempty(PriLev), set as 0.
|}

==Description of Outputs==

{| class="wikitable"
!colspan="2"|The following fields are used:
|-valign="top"
|''x ''||Solution vector with decision variable values (n x 1 vector).
|-valign="top"
|''Inform ''||Result of LSSOL run.

0 = Optimal solution with unique minimizer found.

1 = Weak local solution (nonunique) was reached.

2 = The solution appears to be unbounded.

3 = The constraints could not be satisfied. The problem has no feasible solu- tion.

4 = Too many iterations, in either phase.

5 = 50 changes of working set without change in x, cycling?

6 = An input parameter was invalid.

Other = UNKNOWN LSSOL Inform value.
|-valign="top"
|''iState ''||Status of working set, se input description of iState.
|-valign="top"
|''cLamda ''||Lagrangian multipliers (dual solution vector) (m x 1 vector).
|-valign="top"
|''Iter ''||Number of iterations.
|-valign="top"
|''Ax ''||A*x.
|-valign="top"
|''fObj ''||Value of objective function if feasible, or sum of infeasibilities.
|-valign="top"
|''r ''||Residual for LS problem.
|}

==Using TOMLAB==

'''Purpose'''

''lssolTL ''solves least squares optimization problems defined as

===Calling Syntax===

Using the driver routine ''tomRun '':

<pre>
Prob = ''o''Assign( ... );
Result = tomRun('lssol', Prob ... );
or
Prob = ProbCheck( ... );
Result = lssolTL(Prob);
</pre>

Call Prob = ''o''Assign( ... ) or Prob = ProbDef; to define the Prob for the second option.

===Description of Inputs===

{|class="wikitable"
!colspan="2"|''Prob'', The following fields are used:
|-valign="top"
|''x_L, x_U ''||Bounds on variables.
|-valign="top"
|''b_L, b_U ''||Bounds on linear constraints.
|-valign="top"
|''A ''||Linear constraint matrix.
|-valign="top"
|''QP.c ''||Linear coefficients in objective function.
|-valign="top"
|''QP.F ''||Quadratic matrix of size nnObj x nnObj.
|-valign="top"
|PriLevOpt ''||Print level.
|-valign="top"
|''Warm ''||If true, use warm start, otherwise cold start.
|-valign="top"
|''SOL.xs ''||Solution (and slacks not used) from previous run (Warm start).
|-valign="top"
|''SOL.iState ''||Working set (if Warm start) (n+m) x 1 (DENSE) If length(iState) ¡ n+m, setting iState(1:n+m)=0;

''iState(i)=0: '' Corresponding constraint not in the initial QP working set.

''iState(i)=1: '' Inequality constraint at its lower bound in QP working set.

''iState(i)=2: '' Inequality constraint at its upper bound in QP working set.

''iState(i)=3: '' Equality constraint in the initial QP working set, bl(i)==bu(i).
|-valign="top"
|''SOL.cLamda ''||Lagrangian multipliers from previous run (Warm start).
|-valign="top"
|''SpecsFile ''||Name of user defined SPECS file, read BEFORE optPar() is used.
|-valign="top"
|''PrintFile ''||Name of SOL Print file. Amount and type of printing determined by SPECS parameters or optPar parameters.
|-valign="top"
|''SummFile ''||Name of SOL Summary File.
|-valign="top"
|''optPar ''||Elements ''> ''-999 takes precedence over corresponding TOMLAB params. See Table 50.
|}

===Description of Outputs===

{|class="wikitable"
!colspan="2"|''Result'', The following fields are used:
|-valign="top"
|''Result ''||The structure with results (see ResultDef.m).
|-valign="top"
|''f k ''||Function value at optimum.
|-valign="top"
|''x k ''||Solution vector.
|-valign="top"
|''x 0 ''||Initial solution vector.
|-valign="top"
|''g k ''||Exact gradient computed at optimum.
|-valign="top"
|''xState ''||State of variables. Free == 0; On lower == 1; On upper == 2; Fixed == 3;
|-valign="top"
|''bState ''||State of linear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
|-valign="top"
|''v k ''||Lagrangian multipliers (for bounds + dual solution vector).
|-valign="top"
|''ExitFlag ''||Exit status from lssol.m (similar to TOMLAB).
|-valign="top"
|''Inform ''||LSSOL information parameter.

0 = Optimal solution with unique minimizer found.

1 = Weak local solution (nonunique) was reached.

2 = The solution appears to be unbounded.

3 = The constraints could not be satisfied. The problem has no feasible solu- tion.

4 = Too many iterations, in either phase.

5 = 50 changes of working set without change in x, cycling?

6 = An input parameter was invalid.

Other = UNKNOWN LSSOL Inform value.
|-valign="top"
|''rc ''||Reduced costs. If ninf=0, last m == -v k.
|-valign="top"
|''Iter ''||Number of iterations.
|-valign="top"
|''FuncEv ''||Number of function evaluations. Set to Iter.
|-valign="top"
|''GradEv ''||Number of gradient evaluations. Set to Iter.
|-valign="top"
|''ConstrEv ''||Number of constraint evaluations. Set to 0.
|-valign="top"
|''QP.B ''||Basis vector in TOMLAB QP standard.
|-valign="top"
|''MinorIter''||Number of minor iterations. NOT SET.
|-valign="top"
|''Solver''||Name of the solver (LSSOL).
|-valign="top"
|''SolverAlgorithm ''||Description of the solver.
|-valign="top"
|''SOL.xs ''||Solution and slack variables.
|-valign="top"
|''SOL.cLamda ''||Lagrangian multipliers.
|-valign="top"
|''SOL.iState ''||State for variables and constraints in iState.
|}

==optPar==

===Description===

Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by LSSOL, unless the value is altered in the SPECS file.

===Description of Inputs===

{|class="wikitable"
|+<caption>The following fields are used:</caption>
!#!!SPECS keyword text
!Lower
!Default
!Upper
!Comment
|-
|colspan="2"|'''Printing'''
|-valign="top"
|1.||PRINT LEVEL||0||10||0,1,5,10,20,30
|-valign="top"
|Convergence Tolerances
|-valign="top"
|10.||OPTIMALITY TOLERANCE||''> ''0||1.1E-8||sqrt(eps)
|-valign="top"
|11.||FEASIBILITY TOLERANCE||''> ''0||1.1E-8||sqrt(eps)
|-valign="top"
|Other Tolerances
|-valign="top"
|21.||CRASH TOLERANCE||''> ''0||0.01||''< ''1
|-valign="top"
|27.||RANK TOLERANCE||''> ''0||1.1E-14||100*eps
|-valign="top"
|30.||ITERATIONS LIMIT||''> ''0||max(50,5(n+m))
|-valign="top"
|36.||FEASIBILITY PHASE ITERATIONS||''> ''0||max(50,5(n+m))
|-valign="top"
|45.||INFINITE STEP SIZE||''> ''0||1E20
|-valign="top"
|46.||INFINITE BOUND SIZE||''> ''0||1E20
|}

SOL LSSOL - Revision history

Elias at 15:17, 9 December 2011

Elias at 08:57, 23 August 2011

Elias at 08:41, 23 August 2011

Elias: Created page with "{{Part Of Manual|title=the SOL Manual|link=SOL}} ==Direct Solver Call== A direct solver call is not recommended unless the user is 100 % sure that no other solvers wi..."