Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems

We consider semidefinite monotone linear complementarity problems (SDLCP) in the space ⁿ of real symmetric n×n-matrices equipped with the cone ⁿ₊ of all symmetric positive semidefinite matrices. One may define weighted (using any Mⁿ₊₊ as weight) infeasible interior point paths by replacing the standard condition XY=rI, r>0, (that defines the usual central path) by (XY+YX)/2=rM. Under some mild assumptions (the most stringent is the existence of some strictly complementary solution of (SDLCP)), these paths have a limit as r0, and they depend analytically on all path parameters (such as r and M), even at the limit point r=0.Mathematics Subject Classification (1991): 90C33, 65K05