SOL Solver Reference: Difference between revisions

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{{Part Of Manual|title=the SOL Manual|link=[[SOL|SOL]]}}
{{Part Of Manual|title=the SOL Manual|link=[[SOL|SOL]]}}
The SOL solvers are a set of Fortran solvers that were developed by the Stanford Systems Optimization Laboratory (SOL). <xr id="tab:solSolvers" /> lists the solvers included in TOMLAB  /SOL. The solvers are called using a set of MEX-file interfaces developed as part of TOMLAB. All functionality of the SOL solvers are available and changeable in the TOMLAB framework in Matlab.
The SOL solvers are a set of Fortran solvers that were developed by the Stanford Systems Optimization Laboratory (SOL). [[#Table: The SOL optimization solvers in TOMLAB /SOL.]] lists the solvers included in TOMLAB  /SOL. The solvers are called using a set of MEX-file interfaces developed as part of TOMLAB. All functionality of the SOL solvers are available and changeable in the TOMLAB framework in Matlab.


Detailed descriptions of the TOMLAB  /SOL solvers are given in the following sections. Also see the M-file help for each solver.
Detailed descriptions of the TOMLAB  /SOL solvers are given in the following sections. Also see the M-file help for each solver.
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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>.




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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
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 \MATHSET{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in
\times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in
\MATHSET{R}^{m_1}</math>.
\mathbb{R}^{m_1}</math>.




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</math>
</math>


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




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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>.




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</math>
</math>


where <math>x, x_L, x_U \in \MATHSET{R}^n</math>, <math>r(x) \in \MATHSET{R}^M</math>,
where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>r(x) \in \mathbb{R}^M</math>,
<math>A \in \MATHSET{R}^{m_1 \times n}</math>, <math>b_L,b_U \in
<math>A \in \mathbb{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>.
\mathbb{R}^{m_1}</math> and <math>c_L,c(x),c_U \in \mathbb{R}^{m_2}</math>.
 
====Table: The SOL optimization solvers in TOMLAB /SOL.====


<figtable id="tab:solSolvers">
{| class="wikitable"
{| class="wikitable"
!Function
!Function
!Description
!Description
|-
|+<caption>The SOL optimization solvers in TOMLAB /SOL.</caption>
|-
|-
|''MINOS 5.5''||Sparse linear and nonlinear programming with linear and nonlinear constraints.
|''MINOS 5.5''||Sparse linear and nonlinear programming with linear and nonlinear constraints.
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|''SQOPT 7.1-1''||Sparse convex quadratic programming.
|''SQOPT 7.1-1''||Sparse convex quadratic programming.
|}
|}
</figtable>
 
==MINOS==
*[[SOL MINOS|MINOS]]
 
==LP-MINOS==
*[[SOL LP-MINOS|LP-MINOS]]
 
==QP-MINOS==
*[[SOL QP-MINOS|QP-MINOS]]
 
==LPOPT==
*[[SOL LPOPT|LPOPT]]
 
==QPOPT==
*[[SOL QPOPT|QPOPT]]
 
==LSSOL==
*[[SOL LSSOL|LSSOL]]
 
==NLSSOL==
*[[SOL NLSSOL|NLSSOL]]
 
==NPSOL==
*[[SOL NPSOL|NPSOL]]
 
==SNOPT==
*[[SOL SNOPT|SNOPT]]
 
==SQOPT==
*[[SOL SQOPT|SQOPT]]

Latest revision as of 11:58, 22 January 2012

Notice.png

This page is part of the SOL Manual. See SOL.

The SOL solvers are a set of Fortran solvers that were developed by the Stanford Systems Optimization Laboratory (SOL). #Table: The SOL optimization solvers in TOMLAB /SOL. lists the solvers included in TOMLAB /SOL. The solvers are called using a set of MEX-file interfaces developed as part of TOMLAB. All functionality of the SOL solvers are available and changeable in the TOMLAB framework in Matlab.

Detailed descriptions of the TOMLAB /SOL solvers are given in the following sections. Also see the M-file help for each solver.

The solvers reference guides for the TOMLAB /SOL solvers are available for download from the TOMLAB home page http://tomopt.com. There is also detailed instruction for using the solvers in SOL Using the SOL Solvers in TOMLAB. Extensive TOMLAB m-file help is also available, for example help snoptTL in Matlab will display the features of the SNOPT solver using the TOMLAB format.

TOMLAB /SOL solves nonlinear optimization problems (con) defined as

where , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) \in \mathbb{R}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_L,c(x),c_U \in \mathbb{R}^{m_2}} .


quadratic programming (qp) problems defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\ s/t & \begin{array}{lcccl} x_{L} & \leq & x & \leq & x_{U}, \\ b_{L} & \leq & A x & \leq & b_{U} \\ \end{array} \end{array} }

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c, x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F \in \mathbb{R}^{n \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} .


linear programming (lp) problems defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll} \min\limits_{x} & f(x) = c^T x \\ & \\ s/t & \begin{array}{lcccl} x_{L} & \leq & x & \leq & x_{U}, \\ b_{L} & \leq & A x & \leq & b_{U} \\ \end{array} \end{array} }

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c, x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} .


linear least squares (lls) problems defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} || C x - d || \\ & \\ s/t & \begin{array}{lcccl} x_{L} & \leq & x & \leq & x_{U}, \\ b_{L} & \leq & A x & \leq & b_{U} \\ \end{array} \end{array} }

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d \in \mathbb{R}^M} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C \in \mathbb{R}^{M \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} .


and constrained nonlinear least squares problems defined as

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} r(x)^T r(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} }

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x, x_L, x_U \in \mathbb{R}^n} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r(x) \in \mathbb{R}^M} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \in \mathbb{R}^{m_1 \times n}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \mathbb{R}^{m_1}} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_L,c(x),c_U \in \mathbb{R}^{m_2}} .

Table: The SOL optimization solvers in TOMLAB /SOL.

Function Description
MINOS 5.5 Sparse linear and nonlinear programming with linear and nonlinear constraints.
LP-MINOS A special version of the MINOS 5.5 MEX-file interface for sparse linear programming.
QP-MINOS A special version of the MINOS 5.5 MEX-file interface for sparse quadratic programming.
LPOPT 1.0-10 Dense linear programming.
QPOPT 1.0-10 Non-convex quadratic programming with dense constraint matrix and sparse or dense quadratic matrix.
LSSOL 1.05-4 Dense linear and quadratic programs (convex), and constrained linear least squares problems.
NLSSOL 5.0-2 Constrained nonlinear least squares. NLSSOL is based on NPSOL. No reference except for general NPSOL reference.
NPSOL 5.02 Dense linear and nonlinear programming with linear and nonlinear constraints.
SNOPT 7.1-1 Large, sparse linear and nonlinear programming with linear and nonlinear constraints.
SQOPT 7.1-1 Sparse convex quadratic programming.

MINOS

LP-MINOS

QP-MINOS

LPOPT

QPOPT

LSSOL

NLSSOL

NPSOL

SNOPT

SQOPT

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