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We study two outer approximation schemes, applied to the vari-ational inequality problem in reflexive Banach spaces. First we pro-1 pose a generic outer approximation scheme, and its convergence analysis unifies a wide class of outer approximation methods applied to the constrained optimization problem. As is standard in this setting, boundedness and… (More)

We propose a new kind of inexact scheme for a family of generalized proximal point methods for the monotone complementarity problem. These methods, studied by Auslender, Teboulle and Ben-Tiba, converge under the sole assumption of existence of solutions. We prove convergence of our new scheme, as well as discuss its implementability. Key Words. maximal… (More)

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical… (More)

We propose and analyze an inexact version of the modified subgradient (MSG) algorithm , which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the… (More)