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Semistrictly quasiconvex mappings and non-convex vector optimization

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  • Fabián Flores-Bazán

Abstract

This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with P⊆ [InlineMediaObject not available: see fulltext.] m being the underlying ordering cone, called semistrictly ( [InlineMediaObject not available: see fulltext.] m \ −int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit ( [InlineMediaObject not available: see fulltext.] m \ −int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions. Copyright Springer-Verlag 2004

Suggested Citation

  • Fabián Flores-Bazán, 2004. "Semistrictly quasiconvex mappings and non-convex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 129-145, February.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:129-145
    DOI: 10.1007/s001860300321
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