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2019•SIAM Journal on OptimizationOpen access

On Lipschitz-Like Property for Polyhedral Moving Sets

Ewa M. Bednarczuk, Krzysztof E. Rutkowski

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Abstract

We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on the relaxed constant rank constraint qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this end, we prove the $R$-regularity of the considered set-valued mapping and correct the proof given by these authors.

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We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on the relaxed constant rank constraint qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this end, we prove the $R$-regularity of the considered set-valued mapping and correct the proof given by these authors.

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Available abstract

We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on the relaxed constant rank constraint qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this end, we prove the $R$-regularity of the considered set-valued mapping and correct the proof given by these authors.

Key concepts: Lipschitz continuity, Mathematics, Property (philosophy), Class (philosophy), Constraint (computer-aided design), Set (abstract data type), Constant (computer programming), Rank (graph theory)

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