Merit functions for variational inequality problems
As was remarked upon in Section 1.2, the availability of a merit function for GVIP(F, u, X) which can be evaluated at any point of dom u ∩ X is instrumental for the development of algorithms with mild conditions for convergence; such a merit function can also be an aid in the algorithm itself, both in the selection of step lengths, and in monitoring the convergence of the algorithm through the error bounds that the merit function may supply. This chapter describes and analyzes a family of merit functions which can be constructed for GVIP(F, u, X) and which are evaluated automatically within a CA algorithm.
KeywordsComplementarity Problem Sequential Quadratic Programming Variational Inequality Problem Merit Function Strong Monotonicity
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