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This paper proposes a globally convergent predictor-corrector infeasible-interiorpoint algorithm for the monotone semidenite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.

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We introduce a concept of a strongly stable (Nash) equilibrium point of an n-person noncooperative game in normal form. Roughly speaking, an equilibrium point is strongly stable if it changes continuously and uniquely against any small perturbation to payoffs of players. We establish a necessary and sufficient condition for an equilibrium point to be strongly stable. By the Karush-Kuhn-Tuckcr optimality condition for nonlinear programs, an equilibrium point is shown to correspond to a zero-point of a certain PC1-mapping. Then our condition is stated in terms of the local nonsingularity of the Jacobian matrix of this mapping. Our proof is based on the degree theory of mappings. Finally, we give an example of a 3-person game with two nonquasi-strong equilibrium points, only one of which is strongly stable.

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Let C be a full dimensional, closed, pointed and convex cone in a nite dimensional real vector space E with an inner product hx; yi of x; y 2 E, and M a maximal monotone subset of E 2 E. This paper studies the existence and continuity of centers of the monotone generalized complementarity problem associated with C and M: Find (x; y) 2 M \ (C 2 C 3) such that hx; yi = 0. Here C 3 = fy 2 E : hx; yi 0 for all x 2 Cg denotes the dual cone of C. The main result of the paper unies and extends some results established for monotone complementarity problems in Euclidean space and monotone semidenite linear complementarity problems in symmetric matrices.

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