Evenly Convex Sets: Linear Systems Containing Strict Inequalities

Fajardo, Maria Dolores; Goberna, Miguel Á.; Rodríguez, Margarita M. L.; Vicente-Pérez, José

doi:10.1007/978-3-030-53456-1_1

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Dual Characterizations1

Application To Systems With Strict Convex Inequalities1

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2023

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Cited by 1 publication

(2 citation statements)

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“…A different version of the proof of (iii) can be found in [4,Corollary 1.2]. We also observe that in (iii), we may equivalently write eco R ++ D(σ ) instead of eco D(σ ).…”

Section: Dual Characterizationsmentioning

confidence: 89%

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Duality for Sets of Strong Slater Points

Rodríguez

Vicente-Pérez

2023

Set-Valued Var. Anal

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The strong Slater condition plays a significant role in the stability analysis of linear semi-infinite inequality systems. This piece of work studies the set of strong Slater points, whose non-emptiness guarantees the fullfilment of the strong Slater condition. Given a linear inequality system, we firstly establish some basic properties of the set of strong Slater points. Then, we derive dual characterizations for this set in terms of the data of the system, following similar characterizations provided also for the set of Slater points and the solution set of the given system, which are based on the polarity operators for evenly convex and closed convex sets. Finally, we present two geometric interpretations and apply our results to analyze the strict inequality systems defined by lower semicontinuous convex functions.

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“…A different version of the proof of (iii) can be found in [4,Corollary 1.2]. We also observe that in (iii), we may equivalently write eco R ++ D(σ ) instead of eco D(σ ).…”

Section: Dual Characterizationsmentioning

confidence: 89%

“…We firstly point out that the solution set of τ is not necessarily evenly convex (even when T is singleton). 4. This function is proper lower semicontinuous convex (since the lower level set {(x, y) ∈ dom f : x − √ y ≤ r} is closed and convex for every r ∈ R), and so f = f * * .…”

Section: Application To Systems With Strict Convex Inequalitiesmentioning

confidence: 99%

Duality for Sets of Strong Slater Points

Rodríguez

Vicente-Pérez

2023

Set-Valued Var. Anal

View full text Add to dashboard Cite

show abstract

Evenly Convex Sets: Linear Systems Containing Strict Inequalities

Cited by 1 publication

References 53 publications

Duality for Sets of Strong Slater Points

Duality for Sets of Strong Slater Points

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