First-Order Conditions for C0,1 Constrained Vector Optimization
For a Fritz John type vector optimization problem with C 0,1 data we give scalar characterizations of its solutions applying the so called oriented distance and give necessary and sufficient first order optimality conditions in terms of the Dini derivative. While establishing the sufficiency, we introduce new type of efficient points referred to as isolated minimizers of first order. We show that the obtained necessary conditions are necessary for weak efficiency, and the sufficient conditions are sufficient and under Kuhn-Tucker type constraint qualification also necessary for a point to be an isolated minimizer of first order.
Key wordsVector optimization Nonsmooth optimization C0,1 functions Dini derivatives First-order optimality conditions Lagrange multipliers
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