TOMLAB OPTIMIZATION ENVIRONMENT: lcpAssign

lcpAssign

Purpose

For setting up Linear Complementarity (LCP) problems.

Syntax

   Prob = lcpAssign(M, q, x_L, x_U, x_0, A, b_L, b_U, mu, Name,...
          setupFile, nProblem, x_min, x_max);

Description

lcpAssign is a direct way of setting up a Linear Complementarity Problem (LCP) in the TOMLAB (TQ) format.

The information is put into the TOMLAB input problem structure Prob.

 Prob = lcpAssign(....)

It is then possible to solve the LCP using the TOMLAB PATH solver pathTL with the call:

 Prob = ProbCheck(Prob); Result = pathTL(Prob);

See the file tomlab\examples\testTLlcp1.m and testTLlcp2.m for examples.

lcpAssign may also create an Init File in the TOMLAB Init File format, see the input argument setupFile.

Problem

LCP problem

 
        x >= 0, Mx + q >= 0, x'*(Mx + q) = 0 

        s/t   x_L <=   x  <= x_U
              b_L <= A x  <= b_U

 Equality equations: Set b_L==b_U
 Fixed    variables: Set x_L==x_U

Input Parameters

Two parameters must always be given.

 M:           Matrix n x n.
 q:           Vector n x 1, M and q define the vectors of linear functions.
 x_L          Lower bounds on x. (may be empty), default zeros(n,1).
 x_U          Upper bounds on x. (may be empty)

 x_0          Starting point x.  (may be empty)
 A(m,n)       Polyhedral constraint matrix.                    Default: empty
 b_L          The lower bounds for the polyhedral constraints. Default: empty
 b_U          The upper bounds for the polyhedral constraints. Default: empty
 mu(m)        Starting value for multipliers.                  Default: zero

 Name         The name of the problem (string).
 setupFile    The (unique) name as a TOMLAB Init file. If nonempty lcpAssign
              will create a executable m-file with this name and the given
              problem defined as the first problem in this file.
              See lcp_prob.m, the TOMLAB predefined LCP Init File.
              If empty, no Init File is created.
 nProblem     Number of problems to predefine in the setupFile
              Not used if setupFile is empty.
              If empty assumed to be one. Then text are included in the
              setupFile on how to create additional problems.
              If nProblem > 1,
 x_min        Lower bounds on each x-variable, used for plotting
 x_max        Upper bounds on each x-variable, used for plotting

glcAssign

llsAssign