Closed-Form Expressions for Projectors onto Polyhedral Sets in Hilbert Spaces

DOI10.1137/16M1087540zbMath1378.46020arXiv1607.00102OpenAlexW2607024191MaRDI QIDQ5348473

Krzysztof E. Rutkowski

Publication date: 18 August 2017

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00102

zbMATH Keywords

convex optimizationexplicit solution of optimization problemprojection onto half-spacesquadratic programming problems in Hilbert spaces

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Convex sets in topological vector spaces (aspects of convex geometry) (52A07) Optimality conditions for problems in abstract spaces (49K27)

Related Items

On Lipschitz continuity of projections onto polyhedral moving sets ⋮ Proximal primal-dual best approximation algorithm with memory

Cites Work

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• Iterative methods for fixed point problems in Hilbert spaces
• A new projection method for finding the closest point in the intersection of convex sets
• How to project onto an isotone projection cone
• Iterative methods for nonlinear complementarity problems on isotone projection cones
• Formulations of Support Vector Machines: A Note from an Optimization Point of View
• Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions
• Projection Methods in Conic Optimization
• Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces
• Accelerating the convergence of the method of alternating projections
• An extended projective formula and its application to semidefinite optimization
• Proximité et dualité dans un espace hilbertien
• Nonlinear Programming in Banach Space
• The method of projections for finding the common point of convex sets
• Quadratic Programming in Real Hilbert Spaces
• Orthogonality and Linear Functionals in Normed Linear Spaces
• Convex analysis and monotone operator theory in Hilbert spaces
• Best approximation in inner product spaces