Research articles
ScienceAsia 52 (2026):ID 2026019 1-10 |doi:
10.2306/scienceasia1513-1874..019
Semicontinuity of the sets of approximate solutions for
parametric set optimization problems
Yuhao Zhang, Bo Wei*, Guolin Yu
ABSTRACT: The aim of this paper is to study the semicontinuity of the sets of approximate solutions for parametric
set optimization problems (PSOPs). We use the generalized Hiriart-Urruty oriented distance function to define a
metric in the Hausdorff sense, which allows us to examine the continuity of parametric scalarization functions (PSFs).
Furthermore, we explore the relationship between the solution sets for the PSOPs and the parametric equilibrium
problems (PEPs). We demonstrate that the weak l-minimal approximate solution to the PSOPs is equivalent to the
approximate solution of the PEPs. Finally, the semicontinuity of the solution mappings of the PSOPs is obtained by the
scalarization methods.
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School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021 China |
* Corresponding author, E-mail: weibo_bmd@nmu.edu.cn
Received 10 Dec 2024, Accepted 0 0000
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