2024-03-28T13:12:03Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/485402021-09-05T18:32:42Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
An, Duong Thi Viet
Gutiérrez Vaquero, César
2021-09-03T09:11:12Z
2021-09-03T09:11:12Z
2021
Set-Valued and Variational Analysis, 2021
1877-0533
https://uvadoc.uva.es/handle/10324/48540
10.1007/s11228-021-00601-4
Set-Valued and Variational Analysis
1877-0541
This paper focuses on formulas for the ε-subdifferential of the optimal value function of
scalar and vector convex optimization problems. These formulas can be applied when the
set of solutions of the problem is empty. In the scalar case, both unconstrained problems and
problems with an inclusion constraint are considered. For the last ones, limiting results are
derived, in such a way that no qualification conditions are required. The main mathematical
tool is a limiting calculus rule for the ε-subdifferential of the sum of convex and lower
semicontinuous functions defined on a (non necessarily reflexive) Banach space. In the
vector case, unconstrained problems are studied and exact formulas are derived by linear
scalarizations. These results are based on a concept of infimal set, the notion of cone proper
set and an ε-subdifferential for convex vector functions due to Taa.
eng
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
© 2021 The Authors
Atribución 4.0 Internacional
Differential stability properties in convex scalar and vector optimization
info:eu-repo/semantics/article