Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity

In this paper we study the behavior of infeasible-interior-point-paths for solving horizontal linear complementarity problems that are sufficient in the sense of Cottle et al. (R. W. Cottle, J.-S. Pang, Venkateswaran, Linear Algebra Appl. 114/115 (1989) 231–249). We show that these paths converge to a central point of the set of solutions. It is also shown that these are analytic functions of the path parameter even at the limitpoint, if the complementarity problem has a strictly complementary solution, and have a simple branchpoint, if it is solveable, but has no strictly complementarity solution.

[1]  F. Potra,et al.  Superlinearly Convergent Infeasible-Interior-Point Algorithm for Degenerate LCP , 1998 .

[2]  Josef Stoer,et al.  On the analyticity properties of infeasible-interior-point paths for monotone linear complementarity problems , 1999, Numerische Mathematik.

[3]  Florian A. Potra,et al.  AnO(nL) infeasible-interior-point algorithm for LCP with quadratic convergence , 1996, Ann. Oper. Res..

[4]  H. Väliaho,et al.  P∗-matrices are just sufficient , 1996 .

[5]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[6]  Shinji Mizuno,et al.  Limiting Behavior of Trajectories Generated by a Continuation Method for Monotone Complementarity Problems , 1990, Math. Oper. Res..

[7]  Nimrod Megiddo,et al.  A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems , 1991, Lecture Notes in Computer Science.

[8]  M. Seetharama Gowda,et al.  The extended linear complementarity problem , 1995, Math. Program..

[9]  J. Stoer,et al.  A unified approach to infeasible-interior-point algorithms via geometrical linear complementarity problems , 1996 .

[10]  S. M. Robinson.  Some continuity properties of polyhedral multifunctions , 1981 .

[11]  R. Cottle,et al.  Sufficient matrices and the linear complementarity problem , 1989 .

[12]  Richard W. Cottle,et al.  On a subclass of P0 , 1995 .

[13]  R. Monteiro,et al.  Limiting behavior of the derivatives of certain trajectories associated with a monotone horizontal linear complementarity problem , 1996 .

[14]  G. Sonnevend.  An "analytical centre" for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming , 1986 .

[15]  Florian A. Potra,et al.  A Large-Step Infeasible-Interior-Point Method for the P*-Matrix LCP , 1997, SIAM J. Optim..