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

S.-M. Guu (iesmguu@mail.cgu.edu.tw) and J. Li (junli@cwnu.edu.cn)

Journal of Global Optimization, 2014, vol. 58, issue 4, 767 pages

Abstract: 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. Copyright Springer Science+Business Media New York 2014

Keywords: Image space analysis; Linear separation; Gap functions; Error bounds; Vector quasi-equilibrium problems; 90C; 49J; 65K (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10898-013-0073-y

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