198 lines
3.8 KiB
Matlab
198 lines
3.8 KiB
Matlab
function [z,f,J,mu,status] = pathmcp(z,l,u,cpfj,A,b,t,mu)
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% pathmcp(z,l,u,cpfj,A,b,t,mu)
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%
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% Solve a polyhedrally constrained variational inequality using PATH
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%
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% Calling syntax: [z,f,J] = pathmcp(z,l,u,cpfunjac,A,b,t,mu)
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%
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% Input:
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% z - starting point
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% l - lower bounds on z
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% u - upper bounds on z
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%
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% cpfunjac - the name of the m-file for evaluating the function F and its
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% Jacobian J (without .m-extension).
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%
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% The following m-file must be supplied (where default name is
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% 'mcp_funjac.m' unless stated otherwise in the variable cpfunjac).
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%
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% 'mcp_funjac.m' contains function [f,J,domerr]=cpfunjac(z,jacflag)
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% that computes the function F and if jacflag=1 the sparse
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% Jacobian J at the point z. domerr returns the number of domain
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% violations.
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%
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% A - constraint matrix
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% b - right hand side of the constraints
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% t - types of the constraints
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% <0 : less than or equal
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% =0 : equal to
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% >0 : greater than or equal
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%
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% We have Ax ? b, ? is the type of constraint
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%
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% Output:
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% z - solution
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% mu - multipliers on the constraints
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% f - function evaluation at the solution
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% J - jacobian evaluation at the solution
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Big = 1e20;
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if (nargin < 1)
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error('one input arguments required for mcp(z)');
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end
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z = full(z(:));
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n = length(z);
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if (n == 0)
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error('empty model');
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end
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if (nargin < 2 | isempty(l))
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l = zeros(n,1);
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end
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if (nargin < 3 | isempty(u))
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u = Big*ones(n,1);
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end
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l = full(l(:)); u = full(u(:));
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if (length(l) ~= n | length(u) ~= n)
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error('Input arguments are of incompatible sizes');
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end
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l = max(l,-Big*ones(n,1));
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u = min(u,Big*ones(n,1));
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z = min(max(z,l),u);
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if (nargin < 4 | isempty(cpfj))
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cpfj = 'mcp_funjac';
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end
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m = 0;
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mu = [];
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l_p = [];
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u_p = [];
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if (nargin > 4)
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if (nargin < 6)
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error('Polyhedral constraints require A and b');
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end
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if (~issparse(A))
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A = sparse(A);
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end
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b = full(b(:));
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m = length(b);
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if (m > 0)
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[am, an] = size(A);
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if (am ~= m | an ~= n)
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error('Polyhedral constraints of incompatible sizes');
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end
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if (nargin < 7 | isempty(t))
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t = ones(m,1);
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end
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if (nargin < 8 | isempty(mu))
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mu = zeros(m,1);
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end
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t = full(t(:)); mu = full(mu(:));
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if (length(t) ~= m | length(mu) ~= m)
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error('Polyhedral input arguments are of incompatible sizes');
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end
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l_p = -Big*ones(m,1);
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u_p = Big*ones(m,1);
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idx = find(t > 0);
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if (length(idx) > 0)
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l_p(idx) = zeros(length(idx),1);
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end
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idx = find(t < 0);
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if (length(idx) > 0)
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u_p(idx) = zeros(length(idx),1);
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end
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mu = min(max(mu,l_p),u_p);
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else
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if (nargin >= 8 & ~isempty(mu))
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error('No polyhedral constraints -- multipliers set.');
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end
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if (nargin >= 7 & ~isempty(t))
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error('No polyhedral constraints -- equation types set.');
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end
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end
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else
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A = [];
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end
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% this is a fix, nnz may be bigger than this
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[f,J,domerr] = feval(cpfj,z+1e-5*ones(size(z))+1e-5*abs(z),1);
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if (domerr > 0)
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[f,J,domerr] = feval(cpfj,z,1);
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end
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if (domerr > 0)
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error([cpfj ' not defined at starting point']);
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end
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if ~issparse(J)
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error([cpfj ' must return a sparse Jacobian']);
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end
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nnzJ = nzmax(J);
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row = n + m;
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ele = nnzJ + 2*nzmax(A);
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init = [z; mu];
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low = [l; l_p];
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upp = [u; u_p];
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if m > 0
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global mcp_vifunc;
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global mcp_viconn;
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global mcp_viconm;
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global mcp_viconA;
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global mcp_viconb;
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mcp_vifunc = cpfj;
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mcp_viconn = n;
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mcp_viconm = m;
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mcp_viconA = A;
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mcp_viconb = b;
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[status, ttime, f, J] = mcppath(row, ele, init, low, upp, 'mcp_vifunjac');
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else
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[status, ttime, f, J] = mcppath(row, ele, init, low, upp, cpfj);
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end
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%if (status ~= 1)
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% status,
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% error('Path fails to solve problem');
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%end
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mu = [];
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z = init;
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if m > 0
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mu = init(n+1:n+m);
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z = init(1:n);
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J = J(1:n,1:n);
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f = f(1:n) + A'*mu;
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end
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return;
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