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We consider nonlinear programs with inequality constraints, and we focus on the problem of identifying those constraints which will be active at an isolated local solution. The correct identification of active constraints is important from both a theoretical and a practical point of view. Such an identification removes the combinatorial aspect of the… (More)

An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations with the structure 0 ∈ F (z) + T (z), where T is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type 0 ∈ A(z, s) + T (z). The multifunction A approximates F around s.… (More)

The generalized Nash equilibrium problem, where the feasible sets of the players may depend on the other players' strategies, is emerging as an important modeling tool. However, its use is limited by its great analytical complexity. We consider several Newton methods, analyze their features and compare their range of applicability. We illustrate in detail… (More)

Pairwise classification is the task to predict whether the examples a, b of a pair (a, b) belong to the same class or to different classes. In particular, interclass generalization problems can be treated in this way. In pairwise classification, the order of the two input examples should not affect the classification result. To achieve this, particular… (More)

We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing… (More)

Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We brieey discuss relevant theory associated with the algorithm and describe a sophisticated implementation in… (More)