We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the ($\Phi$, $\rho$)-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential.

### Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems

#### Abstract

We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the ($\Phi$, $\rho$)-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3095509
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