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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)

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)

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)

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)

We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that is weaker than… (More)

We consider a class of Newton-type methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced Linear-Programming-Newton method, designed for the difficult case when solutions need not be isolated, and the equation mapping need not be… (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)