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In this paper we demonstrate how the concept of quasidifferentiability introduced by Demyanov and Rubinov may be extended to the more general concepts of ε-quasidifferentiability and approximate quasidifferentiability. We study the ε-quasidifferentiability of composite functions and present some rules for ε-quasidifferential calculus. The optimality conditions for some typical extremal problems are...
We present first and second order conditions, both necessary and sufficient, for ≺-minimizers of vector-valued mappings over feasible sets with respect to a nontransitive preference relation ≺. Using an analytical representation of a preference relation ≺ in terms of a suitable family of sublinear functions, we reduce the vector optimization problem under study to a scalar inequality, from which,...
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