Abstract
This paper is devoted to the study of optimality conditions for strict minimizers of higher-order for a non-smooth semi-infinite multi-objective optimization problem. We propose a generalized Guignard constraint qualification and a generalized Abadie constraint qualification for this problem under which necessary optimality conditions are proved. Under the assumptions of generalized higher-order strong convexity for the functions appearing in the formulation of the non-smooth semi-infinite multi-objective optimization problem, three sufficient optimality conditions are derived.
Highlights
In recent years, there has been considerable interest in the so-called semi-infinite multiobjective optimization problems (SIMOPs), which is the simultaneous minimization of finitely many scalar objective functions subject to an infinitely many constraints
We introduce the notion of a semi-strict minimizer of higher-order for a semi-infinite multi-objective optimization problem, which includes arbitrary many inequality constraints
For the purpose of investigating this new solution concept, we found that the notion of convexity that appears to be most appropriate in the development of sufficient optimality conditions is the strong convexity of higher-order [ ]
Summary
There has been considerable interest in the so-called semi-infinite multiobjective optimization problems (SIMOPs), which is the simultaneous minimization of finitely many scalar objective functions subject to an infinitely many constraints. In Section , three sufficient optimality conditions for SIMOPs are obtained under the assumption of some generalized strong convexity of higher-order.
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