SOL Solver Reference: Difference between revisions
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</math> | </math> | ||
where <math>x, x_L, x_U \in \ | where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A | ||
\in \ | \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 \ | 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 \ | 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 \ | \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in | ||
\ | \mathbb{R}^{m_1}</math>. | ||
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</math> | </math> | ||
where <math>c, x, x_L, x_U \in \ | 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 \ | \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 \ | where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>d \in \mathbb{R}^M</math>, <math>C | ||
\in \ | \in \mathbb{R}^{M \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math>, | ||
<math>b_L,b_U \in \ | <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 \ | where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>r(x) \in \mathbb{R}^M</math>, | ||
<math>A \in \ | <math>A \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 \mathbb{R}^{m_2}</math>. | ||
<figtable id="tab:solSolvers"> | <figtable id="tab:solSolvers"> |
Revision as of 11:14, 9 December 2011
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 , , , and .
quadratic programming (qp) problems defined as
where , , , and .
linear programming (lp) problems defined as
where , , and .
linear least squares (lls) problems defined as
where , , , , .
and constrained nonlinear least squares problems defined as
where , , , and .
<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>