recspathmcp solves a polyhedrally constrained variational inequality using PATH
Z = recspathmcp(Z,L,U,CPFJ) tries to solve, using Z as a starting point, the mixed
complementarity problem of the form:
L =Z => F(Z)>0,
L<=Z<=U => F(Z)=0,
Z =U => F(Z)<0.
L and U are the lower and upper bounds on Z. recspathmcp returns Z the solution.
CPFJ is the name (without .m-extension) of the m-file for evaluating the
function F and its Jacobian J. The m-file must be supplied (where default name
is 'mcp_funjac.m' unless stated otherwise in the variable
CPFJ). 'mcp_funjac.m' contains function [F,J,DOMERR]=MCP_FUNJAC(Z,JACFLAG)
that computes the function F and if JACFLAG=1 the sparse Jacobian J at the
point Z. DOMERR returns the number of domain violations.
Solver options can be defined through an option file present in the working
directory and named 'path.opt'. Many options are described in the following file:
recspathmcp returns also a log file named 'logfile.tmp'. From MATLAB, it can be
displayed by 'type logfile.tmp'.
Z = recspathmcp(Z,L,U,CPFJ,NNZJ) uses NNZJ the number of non-zero elements in the
Jacobian to initialize the memory allocation for the Jacobian. If NNZJ is not
provided, it is evaluated at the starting point Z.
Z = recspathmcp(Z,L,U,CPFJ,NNZJ,A,B,T,MU)
A - constraint matrix
B - right hand side of the constraints
T - types of the constraints
<0 : less than or equal
=0 : equal to
>0 : greater than or equal
We have AZ ? B, ? is the type of constraint
MU - multipliers on the constraints
[Z,F] = recspathmcp(Z,L,U,CPFJ,...) returns F the function evaluation at the
[Z,F,EXITFLAG] = recspathmcp(Z,L,U,CPFJ,...) returns EXITFLAG that describes
the exit conditions. Possible values listed below.
1 : solved
0 : failed to solve
[Z,F,EXITFLAG,J] = recspathmcp(Z,L,U,CPFJ,...) returns J the Jacobian evaluation
at the solution.
[Z,F,EXITFLAG,J,MU] = recspathmcp(Z,L,U,CPFJ,NNZJ,A,B,T,MU) returns MU the
multipliers on the constraints at the solution.
For more information, see the following references
Dirkse, S. P. and Ferris, M. C. (1995), The PATH solver: A non-monotone
stabilization scheme for mixed complementarity problems, Optimization Methods
and Software 5, 123-156. DOI: 10.1080/10556789508805606
Ferris, M. C. and Munson, T. S. (1999), Interfaces to PATH 3.0: Design,
Implementation and Usage, Computational Optimization and Applications 12,
207-227. DOI: 10.1023/A:1008636318275
Munson, T. S. (2002), Algorithms and Environments for Complementarity, PhD
thesis, University of Wisonsin-Madison.