Weakly upper Lipschitz multifunctions and applications in parametric optimization

Abstract.The main purpose of this paper is to report on our studies of the weak upper Lipschitz and weak φ-upper Lipschitz continuities of multifunctions. Comparisons with other related Lipschitz-type continuities and calmness are given. When the concept of the weak upper Lipschitz continuities is applied to the special cases of constraint multifunctions, such as ones defined by a systems of equalities and inequalities or by a generalized equation we obtain the equivalent conditions with linear functional error bounds. Some results on the perturbation and penalty issues in parametric optimization problems are obtained under weak upper Lipschitz continuity assumptions on the constraint multifunctions. We also discuss the weak φ-upper Lipschitz continuity of a inverse subdifferential.

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