Variational characterization of the contingent epiderivative
نویسندگان
چکیده
In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems. © 2007 Elsevier Inc. All rights reserved.
منابع مشابه
New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems
In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessar...
متن کاملHigher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions
The notions of higher-order weakly generalized contingent epiderivative and higher-order weakly generalized adjacent epiderivative for set-valued maps are proposed. By virtue of the higher-order weakly generalized contingent adjacent epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constrain...
متن کاملFirst-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis
Mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality, so-called “elliptic MPECs”, are formulated in reflexive Banach spaces. With the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures, variational analytic concepts are both applied and further developed. The pap...
متن کاملOptimal Control of Hand, Foot and Mouth Disease Model using Variational Iteration Method
In this paper, the optimal control of transmission dynamics of hand, foot and mouth disease (HFMD), formulated by a compartmental deterministic SEIPR (Susceptible-Incubation (Exposed)- Infected - Post infection virus shedding - Recovered) model with vaccination and treatment as control parameters is considered. The objective function is based on the combination of minimizing the number of infec...
متن کاملHigher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization
A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...
متن کامل