Optimality Conditions and Constraint Qualifications for Quasiconvex Programming

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Abstract

In mathematical programming, various kinds of optimality conditions have been introduced. In the research of optimality conditions, some types of subdifferentials play an important role. Recently, by using Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential, necessary and sufficient optimality conditions for quasiconvex programming have been introduced. On the other hand, constraint qualifications are essential elements for duality theory in mathematical programming. Over the last decade, necessary and sufficient constraint qualifications for duality theorems have been investigated extensively. Recently, by using the notion of generator, necessary and sufficient constraint qualifications for Lagrange-type duality theorems have been investigated. However, constraint qualifications for optimality conditions in terms of Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential have not been investigated yet. In this paper, we study optimality conditions and constraint qualifications for quasiconvex programming. We introduce necessary and sufficient optimality conditions in terms of Greenberg–Pierskalla subdifferential, Martínez-Legaz subdifferential and generators. We investigate necessary and/or sufficient constraint qualifications for these optimality conditions. Additionally, we show some equivalence relations between duality results for convex and quasiconvex programming.

Journal

  • Journal of Optimization Theory and Applications

    Journal of Optimization Theory and Applications 183(3), 963-976, 2019-12

    Springer

Codes

  • NII Article ID (NAID)
    120006949276
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0022-3239
  • Data Source
    IR 
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