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Inner and outer estimates for the solution sets and their asymptotic cones in vector optimization

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Abstract

We use asymptotic analysis to develop finer estimates for the efficient, weak efficient and proper efficient solution sets (and for their asymptotic cones) to convex/quasiconvex vector optimization problems. We also provide a new representation for the efficient solution set without any convexity assumption, and the estimates involve the minima of the linear scalarization of the original vector problem. Some new necessary conditions for a point to be efficient or weak efficient solution for general convex vector optimization problems, as well as for the nonconvex quadratic multiobjective optimization problem, are established.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Fabián Flores-Bazán & Felipe Lara

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  1. Fabián Flores-Bazán
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  2. Felipe Lara
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Correspondence to Fabián Flores-Bazán.

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Flores-Bazán, F., Lara, F. Inner and outer estimates for the solution sets and their asymptotic cones in vector optimization. Optim Lett 6, 1233–1249 (2012). https://doi.org/10.1007/s11590-011-0366-3

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  • DOI: https://doi.org/10.1007/s11590-011-0366-3

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