Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle |
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| Authors: | C. Gutié rrez,L. Thibault |
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| Affiliation: | a Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Edificio de Tecnologías de la Información y las Telecomunicaciones, Paseo de Belén, 15, Campus Miguel Delibes, 47011 Valladolid, Spainb Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, Ciudad Universitaria, 28040 Madrid, Spainc Département des Sciences Mathématiques, Université de Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France |
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| Abstract: | This work deals with strict solutions of set-valued optimization problems under the set optimality criterion. In this context, we introduce a new approximate solution concept and we obtain several properties of these solutions when the error is fixed and also for their limit behavior when the error tends to zero. Then we prove a general existence result, which is applied to obtain approximate Ekeland variational principles. |
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| Keywords: | 49J53 58E30 |
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