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Error Bounds For Regularized Complementarity Problems

By Paul Tseng


An approach to solving a complementarity problem entails regularizing /perturbing the problem by adding to the given mapping another mapping multiplied by a small positive parameter. We study properties of the limit point of the solution to the regularized problem. We also derive local error bounds on the distance from the solution to its limit point, expressed in terms of the regularization parameter. Keywords: Regularization, complementarity problem, optimization, error bound AMS subject classification: 49M39, 90C25, 90C31, 90C34, 90C48 1 Introduction Consider the complementarity problem (CP) of finding an x 2 ! n satisfying x 0; F (x) 0; F (x) T x = 0; (1) where F : ! n + 7! ! n is a given continuous mapping. This is a well-known problem in optimization, with many applications [12, 24]. In various regularization /continuation/smoothing approaches to solving this problem, one adds to the mapping F another mapping G : ! n ++ 7! ! n , multiplied by a small positive sc..

Topics: Regularization, complementarity problem, optimization, error bound
Year: 1998
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