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Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems

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Abstract

This work focuses on the nonemptiness and boundedness of the sets of efficient and weak efficient solutions of a vector optimization problem, where the decision space is a normed space and the image space is a locally convex Hausdorff topological linear space. By studying certain boundedness and coercivity concepts of vector-valued functions and via an asymptotic analysis, we extend to this kind of problems some well-known existence and boundedness results for efficient and weak efficient solutions of multiobjective optimization problems with Pareto or polyhedral orderings. Some of these results are proved under weaker assumptions.

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Acknowledgments

The authors are grateful to the anonymous referees who have contributed to improve the quality of the paper. This research was partially supported by the Ministerio de Economía y Competitividad (Spain) under project MTM2012-30942 (Gutiérrez and Novo) and Conicyt (Chile) under Proyecto Fondecyt 1100919 (López).

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. de Ingenieros de Telecomunicación, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011 , Valladolid, Spain

    César Gutiérrez

  2. Departamento de Matemática y Física Aplicadas, Facultad de Ingeniería, Universidad Católica de la Ssma. Concepción, Alonso de Ribera 2850, Campus San Andrés, Casilla 297, Concepción, Chile

    Rubén López

  3. 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

    Vicente Novo

Authors
  1. César Gutiérrez
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  2. Rubén López
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  3. Vicente Novo
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Correspondence to César Gutiérrez.

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Gutiérrez, C., López, R. & Novo, V. Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems. J Optim Theory Appl 162, 515–547 (2014). https://doi.org/10.1007/s10957-014-0541-7

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  • DOI: https://doi.org/10.1007/s10957-014-0541-7

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