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.