Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings

Gutiérrez, César; Huerga, Lidia; Novo, Vicente; Thibault, Lionel

doi:10.1007/s11228-016-0386-3

Cited by 5 publications

(6 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The next result extends the sequential sum rule in [14,Theorem 3] to more than two functions defined in a not necessarily reflexive Banach space. Although its proof is similar to the one in [14, Theorem 3], we include it for the sake of completeness.…”

Section: Sum Rules For the Approximate Subdifferentialmentioning

confidence: 53%

“…We now give the relationship between qualification condition (14) in Corollary 2 and qualification conditions in [3,Theorem 4.3]. The first assertion is obvious and the second one follows from [29,Lemma 1.58].…”

Section: By Summing Up Both Inequalities and Taking Into Account That γmentioning

confidence: 91%

“…where cl X * denotes the closure for the strong topology on X * . In particular, Theorem 2 reduces to [14,Theorem 3] by considering m = 2 and a reflexive Banach space X.…”

Section: Sum Rules For the Approximate Subdifferentialmentioning

confidence: 99%

“…Proposition 1 Consider a proper function ϕ : X × Y → R and a proper multifunction G : X ⇒ Y . Then the qualification condition (0, 0) ∈ int (domϕ − gphG) implies (14). If, in addition, ϕ and G are convex, then qualification condition ( 14) is equivalent to say that R + (domϕ − gphG) = X × Y .…”

Section: By Summing Up Both Inequalities and Taking Into Account That γmentioning

confidence: 99%

“…It has become an important tool for the study of algorithms as well as for theoretical purposes in convex optimization. For more information, the reader is referred to [14,17,20,28,37] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Differential stability properties in convex scalar and vector optimization

Gutiérrez

2021

Set-Valued Var. Anal

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Sum Rules For the Approximate Subdifferentialmentioning

confidence: 53%

Section: By Summing Up Both Inequalities and Taking Into Account That γmentioning

confidence: 91%

“…where cl X * denotes the closure for the strong topology on X * . In particular, Theorem 2 reduces to [14,Theorem 3] by considering m = 2 and a reflexive Banach space X.…”

Section: Sum Rules For the Approximate Subdifferentialmentioning

confidence: 99%

Section: By Summing Up Both Inequalities and Taking Into Account That γmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Differential stability properties in convex scalar and vector optimization

Gutiérrez

2021

Set-Valued Var. Anal

Self Cite

View full text Add to dashboard Cite

show abstract

Sequential Pareto Subdifferential Sum Rule for Convex Set-Valued Mappings and Applications

Laghdir

Echchaabaoui

2023

J Optim Theory Appl

View full text Add to dashboard Cite

Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Moustaid

Rikouane

Dali

et al. 2021

Rend. Circ. Mat. Palermo, II. Ser

View full text Add to dashboard Cite

In this paper, in the absence of any constraint qualifications, we develop sequential necessary and sufficient optimality conditions for a constrained multiobjective fractional programming problem characterizing a Henig proper efficient solution in terms of the ǫ-subdifferentials and the subdifferentials of the functions. This is achieved by employing a sequential Henig subdifferential calculus rule of the sums of m (m ≥ 2) proper convex vector valued mappings with a composition of two convex vector valued mappings. In order to present an example illustrating the main results of this paper, we establish the classical optimality conditions under Moreau-Rockafellar qualification condition. Our main results are presented in the setting of reflexive Banach space in order to avoid the use of nets.

show abstract

Sequential ε-Subdifferential Calculus for Scalar and Vector Mappings

Cited by 5 publications

References 19 publications

Differential stability properties in convex scalar and vector optimization

Differential stability properties in convex scalar and vector optimization

Sequential Pareto Subdifferential Sum Rule for Convex Set-Valued Mappings and Applications

Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Contact Info

Product

Resources

About