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Necessary and sufficient optimality conditions for set-valued optimization problems. (English) Zbl 1236.90109
Summary: Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by M. C. Travain [Numer. Funct. Anal. Optimization 15, No. 5–6, 689–693 (1994; Zbl 0831.49021)], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange-Fritz-John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.

MSC:
90C29 Multi-objective and goal programming
90C26 Nonconvex programming, global optimization
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