Motzkin decomposition of closed convex sets

DOI10.1016/j.jmaa.2009.10.015zbMath1188.90195OpenAlexW2090226889WikidataQ57836348 ScholiaQ57836348MaRDI QIDQ847066

N. E. Zubov

Publication date: 12 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.10.015

zbMATH Keywords

convex conesconvex setslinear representationpolyhedral setsMotzkin decompositionconic representation

Mathematics Subject Classification ID

Convex programming (90C25) (n)-dimensional polytopes (52B11) Linear programming (90C05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Maximal Quadratic-Free Sets ⋮ The Voronoi inverse mapping ⋮ Unnamed Item ⋮ Weakly Motzkin predecomposable sets ⋮ Recent contributions to linear semi-infinite optimization ⋮ Miguel A. Goberna: ``The challenge was to bring Spanish research in mathematics to normality ⋮ Comments on: Stability in linear optimization and related topics. A personal tour ⋮ Voronoi cells via linear inequality systems ⋮ Projections and generated cones of homothetic convex sets ⋮ On the stability of the Motzkin representation of closed convex sets ⋮ Characterization of tropical hemispaces by \((P, R)\)-decompositions ⋮ Unnamed Item ⋮ Motzkin predecomposable sets ⋮ Recent contributions to linear semi-infinite optimization: an update ⋮ Strong approachability ⋮ Closed convex sets with an open or closed Gauss range ⋮ Strong duality and sensitivity analysis in semi-infinite linear programming ⋮ On OM-decomposable sets ⋮ A relaxation method for solving systems with infinitely many linear inequalities ⋮ On M-predecomposable sets ⋮ Selected applications of linear semi-infinite systems theory ⋮ On Motzkin decomposable sets and functions ⋮ Penumbras and separation of convex sets ⋮ On M-decomposable sets ⋮ Support and separation properties of convex sets in finite dimension ⋮ A subdifferential characterization of Motzkin decomposable functions ⋮ Maximal quadratic-free sets

Cites Work

• Extremal structure of convex sets. II
• Convex analysis and nonlinear optimization. Theory and examples.
• The indirect function of an NTU game
• Representability of convex sets by analytical linear inequality systems.
• On the characterization of some families of closed convex sets
• Recent contributions to linear semi-infinite optimization
• Dual characterizations of set containments with strict convex inequalities
• Excess information in parametric linear optimization
• Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item