Pseudo metric subregularity and its stability in Asplund spaces

Zhang, Binbin; Zhu, Jiangxing

doi:10.1007/s11117-020-00772-8

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…This property is proved to closely relate with error bounds, linear regularity, and basic constraint qualification (BCQ) in optimization and have a huge range of applications in areas of variational analysis and mathematical programming like optimality conditions, variational inequalities, subdifferential theory, the sensitivity analysis of generalized equations and convergence analysis of algorithms for solving equations or inclusions. For these reasons, the concept of the metric subregularity has been extensively studied by many authors (see, e.g., [9,10,11,12,13,14,15,16,17] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Primal criteria of metric subregularity for generalized equations

2022

J. Appl. Numer. Optim.

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This paper is devoted to the study on metric subregularity of a generalized equation defined by a closed set-valued mapping and a closed constraint subset. In terms of Bouligand's contingent cones and tangent derivatives, several primal characterizations and criteria of metric subregularity for the generalized equation are presented with some mild assumptions. This work extends primal results on metric subregularity of the generalized equation from the convex case to the non-convex one.

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Section: Introductionmentioning

confidence: 99%

Primal criteria of metric subregularity for generalized equations

2022

J. Appl. Numer. Optim.

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Convergence analysis of the generalized Douglas-Rachford splitting method under Hölder subregularity assumptions

Zhang

Zhou

Zhu

2023

JIMO

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<p style='text-indent:20px;'>In solving convex optimization and monotone inclusion problems, operator-splitting methods are often employed to transform optimization and inclusion problems into fixed-point equations as the equations obtained from operator-splitting methods are often easy to be solved by standard techniques. For the inclusion problem involving two maximally monotone operators, under the Hölder metric subregularity of the concerned operator, which is weaker than the strong monotonicity of the operator, we derive relationships between the convergence rate of the generalized Douglas-Rachford splitting algorithm and the order of the Hölder metric subregularity of the concerned operator. Moreover, for general multifunctions in Hilbert spaces, by proximal coderivative, we provided some dual sufficient conditions for Hölder metric subregularity.</p>

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Pseudo metric subregularity and its stability in Asplund spaces

Cited by 2 publications

References 28 publications

Primal criteria of metric subregularity for generalized equations

Primal criteria of metric subregularity for generalized equations

Convergence analysis of the generalized Douglas-Rachford splitting method under Hölder subregularity assumptions

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