Step-affine functions, halfspaces, and separation of convex sets with applications to convex optimization problems

DOI10.1134/S008154382103010XzbMath1482.90150OpenAlexW3184640751MaRDI QIDQ2043625

Valentin V. Gorokhovik

Publication date: 3 August 2021

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s008154382103010x

zbMATH Keywords

convex programmingseparation of convex setshalfspacesconvex vector optimization problemsstep-affine functions

Mathematics Subject Classification ID

Convex programming (90C25) Multi-objective and goal programming (90C29)

Cites Work

• On constructing total orders and solving vector optimization problems with total orders
• The generalization of total ordering cones and vectorization to separable Hilbert spaces
• The structure of hemispaces in \({\mathbb{R}}^ n\)
• Classification of semispaces according to their types in infinite-dimensional vector spaces
• Lexicographical separation in \({\mathbb{R}}^ n\)
• Maximal convex sets
• The structure of semispaces
• Convex half-spaces
• Maximal Separation Theorems for Convex Sets
• Ein Beweis des Satzes von M. Eidelheit über konvexe Mengen
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