SOL TOMLAB /SOL Solver Reference
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). <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.
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 (unknown function "\MATHSET"): {\displaystyle x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle f(x) \in \MATHSET{R}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} and Failed to parse (unknown function "\MATHSET"): {\displaystyle c_L,c(x),c_U \in \MATHSET{R}^{m_2}} .
quadratic programming (qp) problems defined as
where Failed to parse (unknown function "\MATHSET"): {\displaystyle c, x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle F \in \MATHSET{R}^{n \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , and Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} .
linear programming (lp) problems defined as
where Failed to parse (unknown function "\MATHSET"): {\displaystyle c, x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , and Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} .
linear least squares (lls) problems defined as
where Failed to parse (unknown function "\MATHSET"): {\displaystyle x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle d \in \MATHSET{R}^M} , Failed to parse (unknown function "\MATHSET"): {\displaystyle C \in \MATHSET{R}^{M \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} .
and constrained nonlinear least squares problems defined as
where Failed to parse (unknown function "\MATHSET"): {\displaystyle x, x_L, x_U \in \MATHSET{R}^n} , Failed to parse (unknown function "\MATHSET"): {\displaystyle r(x) \in \MATHSET{R}^M} , Failed to parse (unknown function "\MATHSET"): {\displaystyle A \in \MATHSET{R}^{m_1 \times n}} , Failed to parse (unknown function "\MATHSET"): {\displaystyle b_L,b_U \in \MATHSET{R}^{m_1}} and Failed to parse (unknown function "\MATHSET"): {\displaystyle c_L,c(x),c_U \in \MATHSET{R}^{m_2}} .
<figtable id="tab:solSolvers">
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. |
</figtable>