Sequential Optimality Conditions for Fractional Optimization with Applications to Vector Optimization

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• 作者：Xiang-Kai Sun (1) (2)
  Xian-Jun Long (1)
  Yi Chai (3)
  
  1. College of Mathematics and Statistics ; Chongqing Technology and Business University ; Chongqing聽 ; 400067 ; China
  2. College of Automation ; Chongqing University ; Chongqing聽 ; 400044 ; China
  3. State Key Laboratory of Power Transmission Equipment and System Security and New Technology ; College of Automation ; Chongqing University ; Chongqing聽 ; 400044 ; China
  
• 关键词：Sequential optimality conditions ; Subdifferential ; Constraint qualification ; Fractional optimization ; Vector optimization ; 90C29 ; 90C32 ; 90C46
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：164
• 期：2
• 页码：479-499
• 全文大小：235 KB
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• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, in the absence of any constraint qualifications, a sequential Lagrange multiplier rule condition characterizing optimality for a fractional optimization problem is obtained in terms of the \(\varepsilon \) -subdifferentials of the functions involved at the minimizer. The significance of this result is that it yields the standard Lagrange multiplier rule condition for the fractional optimization problem under a simple closedness condition that is much weaker than the well-known constraint qualifications. A sequential condition characterizing optimality involving only subdifferentials at nearby points to the minimizer is also investigated. As applications, the proposed approach is applied to investigate sequential optimality conditions for vector fractional optimization problems.