High order infeasible-interior-point methods
for solving sufficient linear complementarity problems
Josef Stoer, Martin Wechs, and Shinji Mizuno
In this paper we develop systematically infeasible-interior-point
methods of arbitrarily high order for solving horizontal linear
complementarity problems that are sufficient in the sense of Cottle,
Pang and Venkateswaran (1989). The results apply to degenerate
problems and problems having no strictly complementary solution.
Variants of these methods are described that eventually avoid
recentering steps, and for which all components of the approximate
solutions converge superlinearly at a high order, and other variants
which even terminate with a solution of the complementarity problem
after finitely many steps.
Research Memorandum 634,
The Institute of Statistical Mathematics, Tokyo, Japan (February, 1997)