Global Newton-type methods and semismooth reformulations for NCP

It is known that a nonlinear complementarity problem (NCP) can be reformulated as a semismooth system of nonlinear equations by using a so called NCP-function. Global Newton-type methods for solving NCP via semismooth reformulation need to use a merit function, which is usually required to be continuously differentiable. In this paper we present a global … Read more

A Bundle Method to Solve Multivalued Variational Inequalities

In this paper we present a bundle method for solving a generalized variational inequality problem. This problem consists in finding a zero of the sum of two multivalued operators defined on a real Hilbert space. The first one is monotone and the second one is the subdifferential of a lower semicontinuous proper convex function. The … Read more

Semismooth Support Vector Machines

The linear support vector machine can be posed as a quadratic program in a variety of ways. In this paper, we look at a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint when the Wolfe dual is taken. The quadratic term is … Read more

On reduced QP formulations of monotone LCP problems

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation—one that has fewer constraints than the “standard” QP formulation—is available. We mention several instances of this class, including the known case in which the … Read more