Semicontinuity Property of Approximate Solution Mappings in Bifunction-Set Optimization

Pham Huu Sach () and Le Anh Tuan ()
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Pham Huu Sach: Institute of Mathematics,Vietnam Academy of Science and Technology
Le Anh Tuan: Nong Lam University

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 8, 202-228

Abstract: Abstract Lower and upper semicontinuity results for the approximate solution mapping of the parametric bifunction-set optimization problem are established under new assumptions that are quite different from the ones used previously in the case of exact solution mapping. Applications to the stability study of the approximate solution mapping of a parametric Kuroiwa set optimization problem and a parametric vector Ky Fan inequality problem are given. To our knowledge, our stability results are original. Several examples are provided.

Keywords: Bifunction-set optimization; Set optimization; Ky Fan inequality; Set-valued map; Semicontinuity; Approximate solution; 90C31; 49K40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01931-x

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