173 lines
3.8 KiB
Matlab
173 lines
3.8 KiB
Matlab
function [z,mu,status] = pathlcp(M,q,l,u,z,A,b,t,mu)
|
|
% pathlcp(M,q,l,u,z,A,b,t,mu)
|
|
%
|
|
% Solve the standard linear complementarity problem using PATH:
|
|
% z >= 0, Mz + q >= 0, z'*(Mz + q) = 0
|
|
%
|
|
% Required input:
|
|
% M(n,n) - matrix
|
|
% q(n) - vector
|
|
%
|
|
% Output:
|
|
% z(n) - solution
|
|
% mu(m) - multipliers (if polyhedral constraints are present)
|
|
%
|
|
% Optional input:
|
|
% l(n) - lower bounds default: zero
|
|
% u(n) - upper bounds default: infinity
|
|
% z(n) - starting point default: zero
|
|
% A(m,n) - polyhedral constraint matrix default: empty
|
|
% b(m) - polyhedral right-hand side default: empty
|
|
% t(m) - type of polyhedral constraint default: 1
|
|
% < 0: less than or equal
|
|
% 0: equation
|
|
% > 0: greater than or equal
|
|
% mu(m) - starting value for multipliers default: zero
|
|
%
|
|
% The optional lower and upper bounds are used to define a linear mixed
|
|
% complementarity problem (box constrained variational inequality).
|
|
% l <= z <= u
|
|
% where l_i < z_i < u_i => (Mz + q)_i = 0
|
|
% l_i = z => (Mz + q)_i >= 0
|
|
% u_i = z => (Mz + q)_i <= 0
|
|
%
|
|
% The optional constraints are used to define a polyhedrally constrained
|
|
% variational inequality. These are transformed internally to a standard
|
|
% mixed complementarity problem. The polyhedral constraints are of the
|
|
% form
|
|
% Ax ? b
|
|
% where ? can be <=, =, or >= depending on the type specified for each
|
|
% constraint.
|
|
|
|
Big = 1e20;
|
|
|
|
if (nargin < 2)
|
|
error('two input arguments required for lcp(M, q)');
|
|
end
|
|
|
|
if (~issparse(M))
|
|
M = sparse(M); % Make sure M is sparse
|
|
end
|
|
q = full(q(:)); % Make sure q is a column vector
|
|
|
|
[mm,mn] = size(M); % Get the size of the inputs
|
|
n = length(q);
|
|
|
|
if (mm ~= mn | mm ~= n)
|
|
error('dimensions of M and q must match');
|
|
end
|
|
|
|
if (n == 0)
|
|
error('empty model');
|
|
end
|
|
|
|
if (nargin < 3 | isempty(l))
|
|
l = zeros(n,1);
|
|
end
|
|
|
|
if (nargin < 4 | isempty(u))
|
|
u = Big*ones(n,1);
|
|
end
|
|
|
|
if (nargin < 5 | isempty(z))
|
|
z = zeros(n,1);
|
|
end
|
|
|
|
z = full(z(:)); l = full(l(:)); u = full(u(:));
|
|
if (length(z) ~= n | length(l) ~= n | length(u) ~= n)
|
|
error('Input arguments are of incompatible sizes');
|
|
end
|
|
|
|
l = max(l,-Big*ones(n,1));
|
|
u = min(u,Big*ones(n,1));
|
|
z = min(max(z,l),u);
|
|
|
|
m = 0;
|
|
if (nargin > 5)
|
|
if (nargin < 7)
|
|
error('Polyhedral constraints require A and b');
|
|
end
|
|
|
|
if (~issparse(A))
|
|
A = sparse(A);
|
|
end
|
|
b = full(b(:));
|
|
|
|
m = length(b);
|
|
|
|
if (m > 0)
|
|
|
|
[am, an] = size(A);
|
|
|
|
if (am ~= m | an ~= n)
|
|
error('Polyhedral constraints of incompatible sizes');
|
|
end
|
|
|
|
if (nargin < 8 | isempty(t))
|
|
t = ones(m,1);
|
|
end
|
|
|
|
if (nargin < 9 | isempty(mu))
|
|
mu = zeros(m,1);
|
|
end
|
|
|
|
t = full(t(:)); mu = full(mu(:));
|
|
if (length(t) ~= m | length(mu) ~= m)
|
|
error('Polyhedral input arguments are of incompatible sizes');
|
|
end
|
|
|
|
l_p = -Big*ones(m,1);
|
|
u_p = Big*ones(m,1);
|
|
|
|
idx = find(t > 0);
|
|
if (length(idx) > 0)
|
|
l_p(idx) = zeros(length(idx),1);
|
|
end
|
|
|
|
idx = find(t < 0);
|
|
if (length(idx) > 0)
|
|
u_p(idx) = zeros(length(idx),1);
|
|
end
|
|
|
|
mu = min(max(mu,l_p),u_p);
|
|
|
|
M = [M -A'; A sparse(m,m)];
|
|
q = [q; -b];
|
|
|
|
z = [z; mu];
|
|
l = [l; l_p];
|
|
u = [u; u_p];
|
|
else
|
|
if (nargin >= 9 & ~isempty(mu))
|
|
error('No polyhedral constraints -- multipliers set.');
|
|
end
|
|
|
|
if (nargin >= 8 & ~isempty(t))
|
|
error('No polyhedral constraints -- equation types set.');
|
|
end
|
|
end
|
|
end
|
|
|
|
idx = find(l > u);
|
|
if length(idx) > 0
|
|
error('Bounds infeasible.');
|
|
end
|
|
|
|
nnzJ = nnz(M);
|
|
|
|
[status, ttime] = lcppath(n+m, nnzJ, z, l, u, M, q);
|
|
|
|
%if (status ~= 1)
|
|
% status,
|
|
% error('Path fails to solve problem');
|
|
%end
|
|
|
|
mu = [];
|
|
if (m > 0)
|
|
mu = z(n+1:n+m);
|
|
z = z(1:n);
|
|
end
|
|
|
|
return;
|
|
|