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Georgiev, Pando

doi:10.1023/a:1008604928549

Cited by 19 publications

(1 citation statement)

References 16 publications

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“…But Rockafellar (1982) and Penot (1996) showed that for all k ≥ 2 the lower -C k functions are lower -C 2 and coincide actually with weakly convex and locally Lipschitz functions. For the role of these classes in optimization we refer also to Georgiev (1997). Later, the uniform notion of ǫ-convex function, due to Jofré, Luc and Théra (1998), allowed Luc, Ngai and Théra (1999) to provide, in terms of a local version of this notion, the robust class of approximately convex functions, characterized in finite dimensions as LC 1 -functions, and then, in Banach spaces by means of submonotonicity of subdifferentials.…”

Section: The Preliminariesmentioning

confidence: 99%

Characterizations and Classification of Paraconvex Multimaps

Mokhtar-Kharroubi¹

2022

Control and Cybernetics

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Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.

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Section: The Preliminariesmentioning

confidence: 99%

Characterizations and Classification of Paraconvex Multimaps

Mokhtar-Kharroubi¹

2022

Control and Cybernetics

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Regularity of a Kind of Marginal Functions in Hilbert Spaces

Pereira

Goncharov

2014

Optimization in Science and Engineering

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and goncha@uevora.pt Dedicated to Panos M. Pardalos in honor of his 60th birthday Summary. We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient.

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