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1 Introduction
1.1 Overview
Welcome to the TOMLAB /PENOPT User's Guide. TOMLAB /PENOPT
includes either PENSDP or PENBMI (depends on the license) and
interfaces between The MathWorks' MATLAB and the solver packages
from PENOPT GbR. The package includes one of the following
solvers:
PENBMI - For large, sparse semidefinite programming problems with
linear and bilinear matrix inequality constraints.
PENSDP - For large, sparse linear semidefinite programming
problems with linear constraints. It also solves feasibility
problems for systems of linear matrix inequalities.
Please visit
http://tomopt.com/tomlab/products/pensdp/,
http://tomopt.com/tomlab/products/penbmi/ and
http://www.penopt.com for more information.
For PENBMI two different input formats may be used for the problem
formulation: The PENBMI Structural Format, an extension of the
PENSDP format for linear problems, and the TOMLAB format for
semidefinite problems. Apart from solving the BMI problem, the
user can check feasibility of the system of linear and bilinear
matrix inequalities.
For PENSDP three different input formats may be used for problem
formulation: The standard sparse SDPA format used in SDPLIB, the
PENSDP Structural Format, and the TOMLAB format for semidefinite
problems.
Problems defined in SeDuMi Matlab format may easily be converted to
SDPA format and solved by TOMLAB /PENSDP. The conversion routine,
called writesdp, was written by Brian Borcher.
Apart from solving the SDP problem, the user can check feasibility
of the system of linear matrix inequalities.
The interface between TOMLAB /PENOPT, Matlab and TOMLAB consists
of two layers. The first layer gives direct access from Matlab
to PENOPT, via calling a Matlab function that calls a
pre-compiled MEX file (DLL under Windows, shared library in UNIX)
that defines and solves the problem in PENOPT. The second layer is
a Matlab function that takes the input in the TOMLAB format, and
calls the first layer function. On return the function creates the
output in the TOMLAB format.
1.2 Contents of this Manual
- Section 2 gives the basic information needed to
run the Matlab interface.
- Section 3 provides all the solver
references for PENBMI and PENSDP.
1.3 Prerequisites
In this manual we assume that the user is familiar with
semidefinite programming, TOMLAB and the Matlab language.
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TOMLAB
