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Full-Text Articles in Applied Mathematics
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho
Mathematics Research Reports
This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
Mathematics Research Reports
This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.
Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study multiobjective optimization problems with equilibrium constraints (MOECs) described by generalized equations in the form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models particularly arise from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex …