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

Peng, Zaiyun; Wang, Ziyuan; Yang, Xinmin

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.

MATHEMATICAL connectedness; INVARIANT sets; MATHEMATICAL equivalence

Journal of Optimization Theory & Applications, 2020, Vol 185, Issue 1, p188

0022-3239

Academic Journal

10.1007/s10957-020-01633-w