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.
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