Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets

Zaiyun Peng (), Ziyuan Wang () and Xinmin Yang ()
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Zaiyun Peng: Chongqing JiaoTong University
Ziyuan Wang: University of British Columbia
Xinmin Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 11, 188-206

Abstract: Abstract In this paper, the connectedness and path-connectedness of solution sets for weak generalized symmetric Ky Fan inequality problems with respect to addition-invariant set are studied. A class of weak generalized symmetric Ky Fan inequality problems via addition-invariant set is proposed. By using a nonconvex separation theorem, the equivalence between the solutions set for the symmetric Ky Fan inequality problem and the union of solution sets for scalarized problems is obtained. Then, we establish the upper and lower semicontinuity of solution mappings for scalarized problem. Finally, the connectedness and path-connectedness of solution sets for symmetric Ky Fan inequality problems are obtained. Our results are new and extend the corresponding ones in the studies.

Keywords: Connectedness; Ky Fan inequality; Lower semicontinuity; Nonlinear scalarization; Addition-invariant set; 49K40; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01633-w

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