Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential

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• 作者：Satoshi Suzuki ; Daishi Kuroiwa
• 关键词：Quasiconvex programming ; Solution set ; Subdifferential ; Optimality condition
• 刊名：Journal of Global Optimization
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：62
• 期：3
• 页码：431-441
• 全文大小：410 KB
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• 作者单位：Satoshi Suzuki (1)
  Daishi Kuroiwa (1)
  
  1. Department of Mathematics, Shimane University, 1060 Nishikawatsu, Matsue, Shimane, Japan
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Science, general
  Real Functions
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1573-2916

文摘

In convex programming, characterizations of the solution set in terms of the subdifferential have been investigated by Mangasarian. An invariance property of the subdifferential of the objective function is studied, and as a consequence, characterizations of the solution set by any solution point and any point in the relative interior of the solution set are given. In quasiconvex programming, however, characterizations of the solution set by any solution point and an invariance property of Greenberg–Pierskalla subdifferential, which is one of the well known subdifferential for quasiconvex functions, have not been studied yet as far as we know. In this paper, we study characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. To the purpose, we show an invariance property of Greenberg–Pierskalla subdifferential, and we introduce a necessary and sufficient optimality condition by Greenberg–Pierskalla subdifferential. Also, we compare our results with previous ones. Especially, we prove some of Mangasarian’s characterizations as corollaries of our results.