1. Locally Lipschitz vector optimization with inequality and equality constraints.
- Author
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Ginchev, Ivan, Guerraggio, Angelo, and Rocca, Matteo
- Subjects
MATHEMATICAL optimization ,MATHEMATICAL analysis ,SIMULATION methods & models ,MATHEMATICS ,LIPSCHITZ spaces - Abstract
The present paper studies the following constrained vector optimization problem: $$\mathop {\min }\limits_C f(x),g(x) \in - K,h(x) = 0$$, where f: ℝ
n → ℝm , g: ℝn → ℝp are locally Lipschitz functions, h: ℝn → ℝq is C1 function, and C ⊂ ℝm and K ⊂ ℝp are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x0 to be a w-minimizer and first-order sufficient conditions for x0 to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done. [ABSTRACT FROM AUTHOR]- Published
- 2010
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