Open AccessStability for semivectorial bilevel programs
Author(s) -
Gaoxi Li,
Liping Tang,
Yingquan Huang,
Xiaoguang Yang
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020161
Subject(s) - bilevel optimization , parametric statistics , stability (learning theory) , mathematical optimization , computer science , upper and lower bounds , set (abstract data type) , parametric programming , solution set , value (mathematics) , mathematics , optimization problem , programming language , mathematical analysis , statistics , machine learning
This paper studies the stability for bilevel program where the lower-level program is a multiobjective programming problem. As we know, the weakly efficient solution mapping for parametric multiobjective program is not generally lower semicontinuous. We first obtain this semicontinuity under a suitable assumption. Then, a new condition for the lower semicontinuity of the efficient solution mapping of this problem is also obtained. Finally, we get the continuities of the value functions and the solution set mapping for the upper-level problem based on the semicontinuities of solution mappings for the lower-level parametric multiobjective program.