Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization

Jiawei Chen (), Elisabeth Köbis (), Markus Köbis () and Jen-Chih Yao ()
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Jiawei Chen: Southwest University
Elisabeth Köbis: Martin Luther University Halle-Wittenberg, Institute of Mathematics
Markus Köbis: Freie universität Berlin
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 13, 816-834

Abstract: Abstract In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinear function is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separation function and a regular weak separation function under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460–479, 2015).

Keywords: Image space analysis; Inverse vector variational inequalities; Multiobjective optimization; Nonlinear separation function; Optimality conditions; 49K05; 90C29 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-017-1197-x

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