Linear regularity, equirregularity, and intersection mappings for convex semi-infinite inequality systems

Cánovas, M. J.; Gómez-Senent, F. J.; Parra, J.

doi:10.1007/s10107-009-0312-7

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Finite Dimensional Theory1

Separable Reduction1

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2013

2024

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Cited by 4 publications

(2 citation statements)

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“…Theorem 6.2 was proved by Dontchev et al in [33] and Theorem 6.3 by Dontchev et al [34]. Theorem 6.5 is a slightly generalized version of the already mentioned result of Cánovas et al [18].…”

Section: Finite Dimensional Theorymentioning

confidence: 72%

See 1 more Smart Citation

Metric Regularity—a Survey Part 1. Theory

Ioffe

2016

J. Aust. Math. Soc.

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Metric regularity theory lies at the very heart of variational analysis, a relatively new discipline whose appearance was, to a large extent, determined by the needs of modern optimization theory in which such phenomena as nondifferentiability and set-valued mappings naturally appear. The roots of the theory go back to such fundamental results of the classical analysis as the implicit function theorem, Sard theorem and some others. This paper offers a survey of the state of the art of some principal parts of the theory along with a variety of its applications in analysis and optimization.

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Section: Finite Dimensional Theorymentioning

confidence: 72%

“…Theorem 5.28 is a new result. A finite-dimensional version of Theorem 5.29 for a class of F with convex graph was proved in [18]. We shall discuss the problems considered in this subsection in more details for finitedimensional mappings later in [61,Section 8].…”

Section: Separable Reductionmentioning

confidence: 99%