SOL Solver Reference: Difference between revisions
No edit summary |
No edit summary |
||
| Line 13: | Line 13: | ||
</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>. | ||
| Line 31: | Line 31: | ||
</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>. | ||
| Line 49: | Line 49: | ||
</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>. | ||
| Line 66: | Line 66: | ||
</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>. | ||
| Line 85: | Line 85: | ||
</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 10:14, 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
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) \\& \\ 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} , , , 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 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}} .
<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>
