Set regularities and feasibility problems

DOI10.1007/s10107-016-1039-xzbMath1390.49012arXiv1602.04935OpenAlexW3099645558MaRDI QIDQ2413089

Nguyen Hieu Thao, D. Russell Luke, Alexander Y. Kruger

Publication date: 6 April 2018

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.04935

zbMATH Keywords

normal conetransversalityHölder regularityfeasibilitymetric regularityalternating projectionsprox-regularityDouglas-RachfordClarke regularityCHIPnormal qualification conditionweak-sharp minima

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Sensitivity, stability, well-posedness (49K40) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Numerical methods based on necessary conditions (49M05) Set-valued and variational analysis (49J53) Numerical methods based on nonlinear programming (49M37)

Related Items (31)

Primal necessary characterizations of transversality properties ⋮ Dual sufficient characterizations of transversality properties ⋮ The projection onto the cross ⋮ Characterizations of some transversality-type properties ⋮ Transversality in variational analysis ⋮ Perturbation of error bounds ⋮ An improved stability result on the metric regularity under Lipschitz set-valued perturbations ⋮ Geometric and metric characterizations of transversality properties ⋮ Regularity of sets under a reformulation in a product space with reduced dimension ⋮ A successive centralized circumcentered-reflection method for the convex feasibility problem ⋮ Exact convergence rates of alternating projections for nontransversal intersections ⋮ Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisited ⋮ Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators ⋮ Random Function Iterations for Consistent Stochastic Feasibility ⋮ Subregular recourse in nonlinear multistage stochastic optimization ⋮ About intrinsic transversality of pairs of sets ⋮ About subtransversality of collections of sets ⋮ A new projection method for finding the closest point in the intersection of convex sets ⋮ A convergent relaxation of the Douglas-Rachford algorithm ⋮ Convex combination of alternating projection and Douglas-Rachford operators for phase retrieval ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Transversality properties: primal sufficient conditions ⋮ Metric inequality conditions on sets and consequences in optimization ⋮ Necessary conditions for linear convergence of iterated expansive, set-valued mappings ⋮ Convergence Analysis of the Relaxed Douglas--Rachford Algorithm ⋮ Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings ⋮ Extremality, stationarity and generalized separation of collections of sets ⋮ On tangential transversality ⋮ Projection methods for high numerical aperture phase retrieval ⋮ Phase Retrieval with Sparse Phase Constraint

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