Optimality conditions for set-valued maps with set optimization |
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Authors: | María Alonso Luis Rodríguez-Marín |
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Institution: | Dpto. Matemática Aplicada I. E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, Aptdo, 60149, 28080 Madrid, Spain |
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Abstract: | Problems in set-valued optimization can be solved via set optimization. In this paper optimality conditions are studied for set-valued maps with set optimization. Optimality requirements are established for continuous selections using directional derivatives. Necessary and sufficient conditions for the existence of solutions are shown for set-valued maps under generalized convexity assumptions and with the notion of the contingent derivative. |
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Keywords: | Set-valued optimization Set optimization Directional derivative Contingent derivative |
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