Set containment characterization for quasiconvex programming

  • Authors:

  • Satoshi Suzuki;Daishi Kuroiwa

  • Affiliations:

  • Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue, Japan and Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue, Japan;Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue, Japan and Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue, Japan

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2009

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Abstract

Dual characterizations of containment of a convex set, defined by quasiconvex constraints, in a convex set, and in a reverse convex set, defined by a quasiconvex constraint, are provided. Notions of quasiconjugate for quasiconvex functions, H-quasiconjugate and R-quasiconjugate, play important roles to derive characterizations of the set containments.