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recspathmcp

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: http://www.cs.wisc.edu/~ferris/path/options.pdf 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 solution. [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.