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). | 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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\mathbb{R}^{m_1}</math> and <math>c_L,c(x),c_U \in \mathbb{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.==== | |||
{| class="wikitable" | {| class="wikitable" | ||
!Function | !Function | ||
!Description | !Description | ||
|- | |- | ||
|''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. | ||
|} | |} | ||
==MINOS== | ==MINOS== | ||
Latest revision as of 11:58, 22 January 2012
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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. |
