RT info:eu-repo/semantics/article
T1 Differential stability properties in convex scalar and vector optimization
A1 An, D. T. V.
A1 Gutiérrez Vaquero, César
K1 Differential stability
K1 ε-subdifferential
K1 Parametric convex programming
K1 Limiting calculus rule
K1 Optimal value function
K1 Approximate solution
K1 Vector optimization
K1 Infimal set
K1 Cone proper set
K1 Weak minimal solution
AB 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 thevector 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.
PB Springer
SN 1877-0533
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/74146
UL https://uvadoc.uva.es/handle/10324/74146
LA eng
NO Set-Valued and Variational Analysis, 2021, vol. 29, n. 4 p. 893-914
NO Producción Científica
DS UVaDOC
RD 08-abr-2025