Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems
We consider semidefinite monotone linear complementarity problems (SDLCP) in the space S-n Of real symmetric n x n-matrices equipped with the cone S-+(n) of all symmetric positive semidefinite matrices. One may define weighted (using any M is an element of S-++(n), as weight) infeasible interior point paths by replacing the standard condition XY = r I, r > 0, (that defines the usual central path) by (XY + YX)/2 = r M. Under some mild assumptions (the most stringent is the existence of some strictly complementary solution of (SDLCP)), these paths have a limit as r down arrow 0, and they depend analytically on all path parameters (such as r and M), even at the limit point r = 0.
linear complementarity problems semidefinite programming infeasible interior-point-paths