Pointwise well-posedness in set optimization with cone proper sets |
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| Authors: | C Gutiérrez |
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| Institution: | a Departamento de Matemática Aplicada, E.T.S. de Ingenieros de Telecomunicación, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011 Valladolid, Spainb Dipartimento di Economia, Università degli Studi dell’Insubria, via Monte Generoso 71, 21100 Varese, Italyc Dipartimento di Economia Politica e Metodi Quantitativi, Università degli Studi di Pavia, via S. Felice 5, 27100 Pavia, Italyd Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal 12, Ciudad Universitaria, 28040 Madrid, Spain |
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| Abstract: | This paper deals with the well-posedness property in the setting of set optimization problems. By using a notion of well-posed set optimization problem due to Zhang et al. (2009) 18] and a scalarization process, we characterize this property through the well-posedness, in the Tykhonov sense, of a family of scalar optimization problems and we show that certain quasiconvex set optimization problems are well-posed. Our approach is based just on a weak boundedness assumption, called cone properness, that is unavoidable to obtain a meaningful set optimization problem. |
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| Keywords: | 49J53 49K40 |
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