On minty variational principle for nonsmooth vector optimization problems with approximate convexity

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• 作者：S. K. Mishra ; Vivek Laha
• 关键词：Nonsmooth vector optimization ; Approximately convex functions ; Clarke subdifferentials ; Approximate vector variational inequalities
• 刊名：Optimization Letters
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：10
• 期：3
• 页码：577-589
• 全文大小：402 KB
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• 作者单位：S. K. Mishra (1)
  Vivek Laha (1)
  
  1. Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operation Research and Decision Theory
  Numerical and Computational Methods in Engineering
  Numerical and Computational Methods
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-4480

文摘

In this paper, we consider a vector optimization problem involving locally Lipschitz approximately convex functions and give several concepts of approximate efficient solutions. We formulate approximate vector variational inequalities of Stampacchia and Minty type and use these inequalities as a tool to characterize an approximate efficient solution of the vector optimization problem.