Displaying similar documents to “Existence of solutions and star-shapedness in generalized Minty variational inequalities in Banach spaces.”

Some new existence, sensitivity and stability results for the nonlinear complementarity problem

Rubén López (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive...

Rescaled proximal methods for linearly constrained convex problems

Paulo J.S. Silva, Carlos Humes (2007)

RAIRO - Operations Research

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We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that ...

An analytic center cutting plane algorithm for finding equilibrium points

Fernanda M.P. Raupp, Wilfredo Sosa (2006)

RAIRO - Operations Research

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We present a variant of the analytic center cutting plane algorithm proposed by Goffin  (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyze the convergence and complexity of the modified algorithm.