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Structure of Pareto Solutions of Generalized Polyhedral‐Valued Vector Optimization Problems in Banach Spaces

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  • Qinghai He
  • Weili Kong

Abstract

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set‐valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

Suggested Citation

  • Qinghai He & Weili Kong, 2013. "Structure of Pareto Solutions of Generalized Polyhedral‐Valued Vector Optimization Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:619206
    DOI: 10.1155/2013/619206
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    References listed on IDEAS

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    1. Ya Ping Fang & Kaiwen Meng & Xiao Qi Yang, 2012. "Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization," Operations Research, INFORMS, vol. 60(2), pages 398-409, April.
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