SOL NPSOL - Revision history

Bjorn: /* Table: The following fields are used: */

2013-08-14T14:31:16Z

Table: The following fields are used:

← Older revision		Revision as of 10:31, 14 August 2013
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	\|17.\|\|STOP CONSTRAINT CHECK AT COL\|\|0\|\|n\|\|n		\|17.\|\|STOP CONSTRAINT CHECK AT COL\|\|0\|\|n\|\|n
	\|-valign="top"		\|-valign="top"
	\|colspan="2"\|''Other Tolerances'''		\|colspan="2"\|'''Other Tolerances'''
	\|-valign="top"		\|-valign="top"
	\|21.\|\|CRASH TOLERANCE		\|21.\|\|CRASH TOLERANCE

	'''Note: Decision variables will be set to the closest bound to the starting point~~'''~~		'''Note: Decision variables will be set to the closest bound to the starting point based on this tolerance before running the optimization.'''
	~~'''~~based on this tolerance before running the optimization~~''''''~~.'''
	\|\|''> ''0\|\|0.01\|\|''< ''1		\|\|''> ''0\|\|0.01\|\|''< ''1
	\|-valign="top"		\|-valign="top"
	\|22.\|\|LINESEARCH TOLERANCE\|\|''> ''0\|\|0.9\|\|''< ''1		\|22.\|\|LINESEARCH TOLERANCE\|\|''> ''0\|\|0.9\|\|''< ''1
	\|-valign="top"		\|-valign="top"
	\|30.\|\|ITERATIONS LIMIT\|\|''> ''0\|\|max(50,3(n+~~m L~~)+10*m_N)		\|30.\|\|ITERATIONS LIMIT\|\|''> ''0\|\|max(50,3(n+m_L)+10*m_N)
	\|-valign="top"		\|-valign="top"
	\|36.\|\|MINOR ITERATIONS LIMIT\|\|''> ''0\|\|max(50,3(n+~~m L~~+m_N))		\|36.\|\|MINOR ITERATIONS LIMIT\|\|''> ''0\|\|max(50,3(n+m_L+m_N))
	\|-valign="top"		\|-valign="top"
	\|37.\|\|STEP LIMIT\|\|''> ''0\|\|2		\|37.\|\|STEP LIMIT\|\|''> ''0\|\|2
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	\|0\|\|3\|\|3\|\|0,1,2,3		\|0\|\|3\|\|3\|\|0,1,2,3
	\|-valign="top"		\|-valign="top"
	\|41.\|\|FUNCTION PRECISION\|\|''> ''0\|\|3.0E-13\|\|''eps''<sup>0''.''8</sup> = ''eps<sub>R</sub>''		\|41.\|\|FUNCTION PRECISION\|\|''> ''0\|\|3.0E-13\|\|''eps''<sup>0''.''8</sup> = ''eps<sub>R</sub>''
	\|-valign="top"		\|-valign="top"
	\|42.\|\|DIFFERENCE INTERVAL\|\|''> ''0\|\|5.48E-8\|\|''eps''<sup>0''.''4</sup>		\|42.\|\|DIFFERENCE INTERVAL\|\|''> ''0\|\|5.48E-8\|\|''eps''<sup>0''.''4</sup>
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	\|45.\|\|INFINITE STEP SIZE\|\|''> ''0\|\|max(BIGBND,1E10)		\|45.\|\|INFINITE STEP SIZE\|\|''> ''0\|\|max(BIGBND,1E10)
	\|-valign="top"		\|-valign="top"
	\|46.\|\|INFINITE BOUND SIZE\|\|''> ''0\|\|1E10\|\|= BIGBND,		\|46.\|\|INFINITE BOUND SIZE\|\|''> ''0\|\|1E10\|\|= BIGBND
	\|-valign="top"		\|-valign="top"
	\|50.\|\|HESSIAN YES or NO\|\|0\|\|0\|\|1 = YES		\|50.\|\|HESSIAN YES or NO\|\|0\|\|0\|\|1 = YES
	\|}		\|}

Bjorn: /* Description of Inputs */

2013-08-14T14:22:19Z

Description of Inputs

← Older revision		Revision as of 10:22, 14 August 2013
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	\|''SOL.iState''\|\|Working set (if Warm start) (n+m) x 1 (DENSE) If length(iState) ¡ n+m, setting iState(1:n+m)=0;		\|''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)=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)=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)=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).		''iState(i)=3:'' Equality constraint in the initial QP working set, bl(i)==bu(i).
	\|-valign="top"		\|-valign="top"
	\|''SOL.cLamda ''\|\|Lagrangian multipliers (dual solution vector) (nb x 1 vector).		\|''SOL.cLamda''\|\|Lagrangian multipliers (dual solution vector) (nb x 1 vector).
	\|-valign="top"		\|-valign="top"
	\|''SOL.H ''\|\|Cholesky factor of Hessian approximation Hessian no - reordered variables ~~Hes- sian~~ yes - natural order of variables, used for Warm start.		\|''SOL.H''\|\|Cholesky factor of Hessian approximation Hessian no - reordered variables. Hessian yes - natural order of variables, used for Warm start.
	\|-valign="top"		\|-valign="top"
	\|''SOL.SpecsFile ''\|\|Name of user defined SPECS file, read BEFORE optPar() is used.		\|''SOL.SpecsFile ''\|\|Name of user defined SPECS file, read BEFORE optPar() is used.

Bjorn: /* Description of Inputs */

2013-08-14T14:15:18Z

Description of Inputs

← Older revision		Revision as of 10:15, 14 August 2013
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	Prob.P = ProblemNumber, where ProblemNumber is some integer. Two user written routines must be written:		Prob.P = ProblemNumber, where ProblemNumber is some integer. Two user written routines must be written:

	funfdf, actual name stored in Prob.FUNCS.fg, with syntax [mode, f, g] =		funfdf, actual name stored in Prob.FUNCS.fg, with syntax [mode, f, g] = funfdf(x, Prob, mode, nstate).

	~~funfdf(x, Prob, mode, nstate).~~		funcdc, actual name stored in Prob.FUNCS.cdc, with syntax [mode, c, dc] = funcdc(x, Prob, mode, nstate).

	funcdc, actual name stored in Prob.FUNCS.cdc, with syntax [mode, c, dc] =

	funcdc(x, Prob, mode, nstate).

	NPSOL is calling the TOMLAB routines nlp fg.m and nlp cdc.m in the call- back, and they call funfdf and funcdc, respectively.		NPSOL is calling the TOMLAB routines nlp fg.m and nlp cdc.m in the call- back, and they call funfdf and funcdc, respectively.
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	\|''Warm ''\|\|Flag for Warm start (==1) or Cold Start (==0 ), i.e. normal mode. If 'WarmStart', iState, cLamda, H and x must supply correct values.		\|''Warm ''\|\|Flag for Warm start (==1) or Cold Start (==0 ), i.e. normal mode. If 'WarmStart', iState, cLamda, H and x must supply correct values.
	\|-valign="top"		\|-valign="top"
	\|''H ''\|\|Hessian matrix, only accessed if Warm start. Must select: Hessian = Yes in order to do a warm start Hessian Yes is equivalent to optPar(50) = 1 (default is 0).		\|''H ''\|\|Hessian matrix, only accessed if Warm start. Must select: Hessian = Yes in order to do a warm start. Hessian Yes is equivalent to optPar(50) = 1 (default is 0).
	\|-valign="top"		\|-valign="top"
	\|''iState ''\|\|Working set (if Warm start) (nb = n+nclin+ncnln) x 1 (DENSE). If length(iState) ''< ''nb, setting iState(1:nb)=0;;		\|''iState ''\|\|Working set (if Warm start) (nb = n+nclin+ncnln) x 1 (DENSE). If length(iState) ''< ''nb, setting iState(1:nb)=0;

	''iState(i)=0: ''\|\|Corresponding constraint not in the initial working set.		''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)=1:'' Inequality constraint at its lower bound in working set.

	''iState(i)=2: ''\|\|Inequality constraint at its upper 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).		''iState(i)=3:'' Equality constraint in the initial working set, bl(i)==bu(i).
	\|-valign="top"		\|-valign="top"
	\|''cLamda ''\|\|Lagrangian multipliers for the n + nclin + ncnln constraints. If Warm start, cLamda(n+nclin+1:n+nclin+ncnln), the nonlinear Lagrange multipliers, must correspond to values in iState.		\|''cLamda ''\|\|Lagrangian multipliers for the n + nclin + ncnln constraints. If Warm start, cLamda(n+nclin+1:n+nclin+ncnln), the nonlinear Lagrange multipliers, must correspond to values in iState.
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	\|''PrintFile ''\|\|Name of the Print file. Name includes the path, maximal number of characters = 500.		\|''PrintFile ''\|\|Name of the Print file. Name includes the path, maximal number of characters = 500.
	\|-valign="top"		\|-valign="top"
	\|''SummFile ''\|\|Name of the Summary file. Name includes the path, maximal number of ~~char- acters~~ = 500.		\|''SummFile ''\|\|Name of the Summary file. Name includes the path, maximal number of characters = 500.
	\|-valign="top"		\|-valign="top"
	\|''PriLev ''\|\|Print level in the npsol MEX-interface.		\|''PriLev ''\|\|Print level in the npsol MEX-interface.

Bjorn: /* Purpose */

2013-08-14T13:54:56Z

Purpose

← Older revision		Revision as of 09:54, 14 August 2013
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	\end{array}		\end{array}
	</math>		</math>


	where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A		where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A

Elias at 16:30, 21 January 2012

2012-01-21T16:30:11Z

← Older revision		Revision as of 12:30, 21 January 2012
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	===Description of Inputs===		===Description of Inputs===

	~~<figtable id~~=~~"tab~~:~~specs">~~		====Table: The following fields are used:====

	{\|class="wikitable"		{\|class="wikitable"
	~~\|+<caption>The following fields are used:</caption>~~
	!#!!SPECS keyword text		!#!!SPECS keyword text
	!Lower		!Lower
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	\|50.\|\|HESSIAN YES or NO\|\|0\|\|0\|\|1 = YES		\|50.\|\|HESSIAN YES or NO\|\|0\|\|0\|\|1 = YES
	\|}		\|}
	~~</figtable>~~

Elias at 18:05, 8 December 2011

2011-12-08T18:05:21Z

← Older revision		Revision as of 14:05, 8 December 2011
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	</math>		</math>

	where <math>x, x_L, x_U \in \~~MATHSET~~{R}^n</math>, <math>f(x) \in \~~MATHSET~~{R}</math>, <math>A		where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A
	\in \~~MATHSET~~{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \~~MATHSET~~{R}^{m_1}</math>		\in \mathbb{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \mathbb{R}^{m_1}</math>
	and <math>c_L,c(x),c_U \in \~~MATHSET~~{R}^{m_2}</math>.		and <math>c_L,c(x),c_U \in \mathbb{R}^{m_2}</math>.

	===Calling Syntax===		===Calling Syntax===
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	</math>		</math>

	where <math>x, x_L, x_U \in \~~MATHSET~~{R}^n</math>, <math>f(x) \in \~~MATHSET~~{R}</math>, <math>A		where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A
	\in \~~MATHSET~~{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \~~MATHSET~~{R}^{m_1}</math>		\in \mathbb{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \mathbb{R}^{m_1}</math>
	and <math>c_L,c(x),c_U \in \~~MATHSET~~{R}^{m_2}</math>.		and <math>c_L,c(x),c_U \in \mathbb{R}^{m_2}</math>.

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

Elias at 13:59, 25 August 2011

2011-08-25T13:59:19Z

← Older revision		Revision as of 09:59, 25 August 2011
Line 2:		Line 2:
	==Direct Solver Call==		==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 3.8.2~~ for information on how to use NPSOL 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 NPSOL with TOMLAB.

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

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 will..."

2011-08-23T13:35:19Z

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 will..."

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 3.8.2 for information on how to use NPSOL with TOMLAB.

===Purpose===

''npsol ''solves dense nonlinear optimization problems defined as

<math>
\begin{array}{ll}
\min\limits_{x} & f(x) \\
& \\
s/t & \begin{array}{lcccl}
x_{L} & \leq & x & \leq & x_{U}, \\
b_{L} & \leq & A x & \leq & b_{U} \\
c_{L} & \leq & c(x) & \leq & c_{U} \\
\end{array}
\end{array}
</math>

where <math>x, x_L, x_U \in \MATHSET{R}^n</math>, <math>f(x) \in \MATHSET{R}</math>, <math>A
\in \MATHSET{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \MATHSET{R}^{m_1}</math>
and <math>c_L,c(x),c_U \in \MATHSET{R}^{m_2}</math>.

===Calling Syntax===

The file 'funfdf.m' must be defined and contain: function [mode, f, g] = funfdf(x, Prob, mode, nstate) to compute the objective function f and the gradient g at the point x.

The file 'funcdc.m' must be defined and contain: function [mode, c ,dcS] = funcdc(x, Prob, mode, nstate) to compute the nonlinear constraint value c and the constraint Jacobian dcS for the nonlinear constraints at the point x.

<pre>
[x, Inform, iState, cLamda, iwCount, fObj, gObj, fCon, gCon, H] = npsol( A, bl, bu, x,
Prob, optPar, Warm, H, iState, cLamda, SpecsFile, PrintFile, SummFile, PriLev, ProbName );
</pre>

===Description of Inputs===

{|class="wikitable"
!colspan="2"|The following fields are used:
|-valign="top"
|''A''||Constraint matrix, m x n. (DENSE).
|-valign="top"
|''bl ''||Lower bounds on (x,Ax,c(x)).
|-valign="top"
|''bu ''||Upper bounds on (x,Ax,c(x)).
|-valign="top"
|''x ''||Initial x vector (n x 1). If Warm start x must correspond to values in H and iState.
|-valign="top"
|''Prob ''||Must be a structure. No check is made in the MEX interface.

If TOMLAB calls npsol, then Prob is the standard TOMLAB problem struc- ture, otherwise the user should set:

Prob.P = ProblemNumber, where ProblemNumber is some integer. Two user written routines must be written:

funfdf, actual name stored in Prob.FUNCS.fg, with syntax [mode, f, g] =

funfdf(x, Prob, mode, nstate).

funcdc, actual name stored in Prob.FUNCS.cdc, with syntax [mode, c, dc] =

funcdc(x, Prob, mode, nstate).

NPSOL is calling the TOMLAB routines nlp fg.m and nlp cdc.m in the call- back, and they call funfdf and funcdc, respectively.

If these fields in Prob are empty (Prob.FUNCS.fg, Prob.FUNCS.cdc), the TOMLAB callback routines calls the usual function routines. Then the Prob struct should be normally defined, and the fields Prob.FUNCS.f, Prob.FUNCS.g, Prob.FUNCS.c, Prob.FUNCS.dc be set in the normal way (e.g. by the routine mFiles.m, or one of the Assign-routines like conAssign.m).

If the mode parameter is 0, funfdf should return f, otherwise both f and the gradient vector g. If the mode parameter is 0, funcdc should return c, otherwise both c and dc. Note that each row in dc corresponds to a constraint, and that dc should be a dense matrix. If the matrix dc is returned as a sparse Matlab matrix, nlp cdc will do full(dc) to get a dense matrix.

The user could also write his own versions of the routines nlp fg.m and nlp cdc.m and put them before in the path.
|-valign="top"
|''optPar ''||Vector with optimization parameters overriding defaults and the optionally specified SPECS file. Set empty if only using default parameters.
|-valign="top"
|''Warm ''||Flag for Warm start (==1) or Cold Start (==0 ), i.e. normal mode. If 'WarmStart', iState, cLamda, H and x must supply correct values.
|-valign="top"
|''H ''||Hessian matrix, only accessed if Warm start. Must select: Hessian = Yes in order to do a warm start Hessian Yes is equivalent to optPar(50) = 1 (default is 0).
|-valign="top"
|''iState ''||Working set (if Warm start) (nb = n+nclin+ncnln) x 1 (DENSE). If length(iState) ''< ''nb, setting iState(1:nb)=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"
|''cLamda ''||Lagrangian multipliers for the n + nclin + ncnln constraints. If Warm start, cLamda(n+nclin+1:n+nclin+ncnln), the nonlinear Lagrange multipliers, must correspond to values in iState.
|-valign="top"
|''SpecsFile ''||Name of the input parameter 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 char- acters = 500.
|-valign="top"
|''PriLev ''||Print level in the npsol MEX-interface.

= 0 Silent

= 10 Dimensions are printed.
|-valign="top"
|''ProbName ''||Name of the problem. ¡=100 characters are used in the MEX interface. (Not used by MEX-interface).
|}

===Description of Outputs===

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

0 = Optimal solution found.

1 = Optimal solution found but not to requested accuracy.

2 = No feasible point for the linear constraints.

3 = No feasible point for the nonlinear constraints.

4 = Too many major iterations.

6 = The current point cannot be improved on.

7 = Large errors found in the derivatives.

9 = An input parameter is invalid. Other = User requested termination
|-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"
|''iwCount ''||Number of iterations (iwCount(1)), function evaluations (iwCount(2)) and constraint evaluations (iwCount(3)).
|-valign="top"
|''fObj ''||Objective function value at optimum. ''gObj ''Gradient of the nonlinear objective.
|-valign="top"
|''fCon ''||Nonlinear constraint vector.
|-valign="top"
|''gCon ''||Gradient matrix of the nonlinear constraint vector.
|-valign="top"
|''H ''||Cholesky factor of Hessian approximation. Hessian no-reordered variables. Hessian yes - natural order of variables, used for Warm start.
|}

==Using TOMLAB==

===Purpose===

''npsolTL ''solves dense nonlinear optimization problems defined as

<math>
\begin{array}{ll}
\min\limits_{x} & f(x) \\
& \\
s/t & \begin{array}{lcccl}
x_{L} & \leq & x & \leq & x_{U}, \\
b_{L} & \leq & A x & \leq & b_{U} \\
c_{L} & \leq & c(x) & \leq & c_{U} \\
\end{array}
\end{array}
</math>

where <math>x, x_L, x_U \in \MATHSET{R}^n</math>, <math>f(x) \in \MATHSET{R}</math>, <math>A
\in \MATHSET{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \MATHSET{R}^{m_1}</math>
and <math>c_L,c(x),c_U \in \MATHSET{R}^{m_2}</math>.

===Calling Syntax===

Using the driver routine ''tomRun '':

<pre>
Prob = ''o''Assign( ... );
Result = tomRun('npsol', Prob ... );
</pre>

===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"
|''c_L, c_U''||Bounds on nonlinear constraints. ''A ''Linear constraint matrix.
|-valign="top"
|''PriLevOpt''||Print level.
|-valign="top"
|''WarmStart''||If true, use warm start, otherwise cold start.
|-valign="top"
|''SOL.xs''||Solution from previous run, elements xs[1:n].
|-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 (dual solution vector) (nb x 1 vector).
|-valign="top"
|''SOL.H ''||Cholesky factor of Hessian approximation Hessian no - reordered variables Hes- sian yes - natural order of variables, used for Warm start.
|-valign="top"
|''SOL.SpecsFile ''||Name of user defined SPECS file, read BEFORE optPar() is used.
|-valign="top"
|''SOL.PrintFile ''||Name of SOL Print file. Amount and type of printing determined by SPECS parameters or optPar parameters.
|-valign="top"
|''SOL.SummFile ''||Name of SOL Summary File.
|-valign="top"
|''SOL.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 ''||Gradient of the function.
|-valign="top"
|''c_k ''||Nonlinear constraint residuals.
|-valign="top"
|''cJac ''||Nonlinear constraint gradients.
|-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"
|''cState''||State of nonlinear 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 npsol.m (similar to TOMLAB).
|-valign="top"
|''Inform ''||NPSOL information parameter.

0 = Optimal solution found.

1 = Optimal solution found but not to requested accuracy.

2 = No feasible point for the linear constraints.

3 = No feasible point for the nonlinear constraints.

4 = Too many major iterations.

6 = The current point cannot be improved on.

7 = Large errors found in the derivatives.

9 = An input parameter is invalid. Other = User requested termination
|-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.
|-valign="top"
|''GradEv''||Number of gradient evaluations.
|-valign="top"
|''ConstrEv''||Number of constraint evaluations.
|-valign="top"
|''QP.B ''||Basis vector in TOMLAB QP standard.
|-valign="top"
|''MinorIter''||Number of minor iterations.
|-valign="top"
|''Solver''||Name of the solver (npsol).
|-valign="top"
|''SolverAlgorithm''||Description of the solver.
|-valign="top"
|''SOL.x''||Solution vector (n by 1) with n decision variable values.
|-valign="top"
|''SOL.iState''||basis status of constraints + variables, (m + n x 1 vector). State of variables:

0=nonbasic (on bl), 1=nonbasic (on bu), 2=superbasic (between bounds),

3=basic (between bounds).
|-valign="top"
|''SOL.cLamda''||Lagrangian multipliers (dual solution vector) (m x 1 vector).
|-valign="top"
|''SOL.H''||Cholesky factor of Hessian approximation. Hessian no - reordered variables. Hessian yes - natural order of variables, used for Warm start.
|}

==optPar==

===Description===

Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by NPSOL, if not the value is altered in the SPECS file (input SpecsFile).

===Description of Inputs===

<figtable id="tab:specs">
{|class="wikitable"
|+<caption>The following fields are used:</caption>
!#!!SPECS keyword text
!Lower
!Default
!Upper
!Comment
|-valign="top"
|colspan="2"|'''Printing'''
|-valign="top"
|1.||PRINT LEVEL

or MAJOR PRINT LEVEL
||0||10||||0,1,5,10,20,30
|-valign="top"
|2.||MINOR PRINT LEVEL||0||0||||0,1,5,10,20,30
|-valign="top"
|colspan="2"|'''Convergence Tolerances'''
|-valign="top"
|9.||NONLINEAR FEASIBILITY TOLERANCE||''> ''0||1.1E-8||||sqrt(eps)
|-valign="top"
|10.||OPTIMALITY TOLERANCE||''> ''0||3.0E-13||||''eps''0''.''8
|-valign="top"
|11.||LINEAR FEASIBILITY TOLERANCE||''> ''0||||1.1E-8||sqrt(eps)
|-valign="top"
|colspan="2"|'''Derivative checking'''
|-valign="top"
|13.||VERIFY LEVEL||-1||-1||3||-1,0,1,2,3
|-valign="top"
|14.||START OBJECTIVE CHECK AT COL||0||1||n
|-valign="top"
|15.||STOP OBJECTIVE CHECK AT COL||0||n||n
|-valign="top"
|16.||START CONSTRAINT CHECK AT COL||0||1||n
|-valign="top"
|17.||STOP CONSTRAINT CHECK AT COL||0||n||n
|-valign="top"
|colspan="2"|''Other Tolerances'''
|-valign="top"
|21.||CRASH TOLERANCE

'''Note: Decision variables will be set to the closest bound to the starting point'''
'''based on this tolerance before running the optimization''''''.'''
||''> ''0||0.01||''< ''1
|-valign="top"
|22.||LINESEARCH TOLERANCE||''> ''0||0.9||''< ''1
|-valign="top"
|30.||ITERATIONS LIMIT||''> ''0||max(50,3(n+m L)+10*m_N)
|-valign="top"
|36.||MINOR ITERATIONS LIMIT||''> ''0||max(50,3(n+m L+m_N))
|-valign="top"
|37.||STEP LIMIT||''> ''0||2
|-valign="top"
|39.||DERIVATIVE LEVEL

Is set by npsolTL dependent on Prob.ConsDiff, Prob.NumDiff
|0||3||3||0,1,2,3
|-valign="top"
|41.||FUNCTION PRECISION||''> ''0||3.0E-13||''eps''0''.''8 = ''epsR''
|-valign="top"
|42.||DIFFERENCE INTERVAL||''> ''0||5.48E-8||''eps''0''.''4
|-valign="top"
|43.||CENTRAL DIFFERENCE INTERVAL||''> ''0||6.70E-5||''eps''0''.''8''/''3
|-valign="top"
|45.||INFINITE STEP SIZE||''> ''0||max(BIGBND,1E10)
|-valign="top"
|46.||INFINITE BOUND SIZE||''> ''0||1E10||= BIGBND,
|-valign="top"
|50.||HESSIAN YES or NO||0||0||1 = YES
|}
</figtable>