Vector quasi-equilibrium problems: separation, saddle points and error bounds for the solution set

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• 作者：S.-M. Guu (1)
  J. Li (2)
  
• 关键词：Image space analysis ; Linear separation ; Gap functions ; Error bounds ; Vector quasi ; equilibrium problems ; 90C ; 49J ; 65K
• 刊名：Journal of Global Optimization
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：58
• 期：4
• 页码：751-767
• 全文大小：241 KB
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• 作者单位：S.-M. Guu (1)
  J. Li (2)
  
  1. Graduate Institute of Business and Management, College of Management, Chang-Gung University, Kwei-Shan, Taoyuan Hsien, 333, Taiwan
  2. College of Mathematics and Information, China West Normal University, Nanchong, 637009, Sichuan, China
  
• ISSN：1573-2916

文摘

In this paper, we employ the image space analysis (for short, ISA) to investigate vector quasi-equilibrium problems (for short, VQEPs) with a variable ordering relation, the constrained condition of which also consists of a variable ordering relation. The quasi relatively weak VQEP (for short, qr-weak VQEP) are defined by introducing the notion of the quasi relative interior. Linear separation for VQEP (res., qr-weak VQEP) is characterized by utilizing the quasi interior of a regularization of the image and the saddle points of generalized Lagrangian functions. Lagrangian type optimality conditions for VQEP (res., qr-weak VQEP) are then presented. Gap functions for VQEP (res., qr-weak VQEP) are also provided and moreover, it is shown that an error bound holds for the solution set of VQEP (res., qr-weak VQEP) with respect to the gap function under strong monotonicity.