Maximization of lower semi-continuous convex functionals on bounded subsets of locally convex spaces. I: Hyperplane theorems

DOI10.1007/BF01442563zbMath0421.90077MaRDI QIDQ1133473

Ivan Singer

Publication date: 1979

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

zbMATH Keywords

locally convex spacesapproximation theorylower semicontinuous convex functionalconvex functionalssupport hyperplanes

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) General theory of locally convex spaces (46A03)

Related Items (12)

Lagrangian duality theorems for reverse convex infimization ⋮ Duality in quasi-convex supremization and reverse convex infimization via abstract convex analysis,and applications to approximation ** ⋮ Necessary and sufficient global optimality conditions for convex maximization revisited ⋮ Optimality Conditions for the Minimization of Quadratic 0-1 Problems ⋮ Duality theorems for linear systems and convex systems ⋮ Optimization by level set methods vi:generalizations of surrogate type reverse convex duality ⋮ Maximization of lower semi-continuous convex functionals on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems ⋮ Duality theorems for perturbed convex optimization ⋮ Extensions of functions of 0-1 variables and applications to combinatorial optimization ⋮ Unnamed Item ⋮ On farthest Voronoi cells ⋮ Zur existenz von lösungen konvexer optimierungsaufgaben in lokalkonvexen räumen

Cites Work

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• Duality theorems for linear systems and convex systems
• Maximization of lower semi-continuous convex functionals on bounded subsets of locally convex spaces. II: Quasi-Lagrangian duality theorems
• Generalizations of methods of best approximation to convex optimization in locally convex spaces. II: hyperbolic theorems
• Some new applications of the Fenchel-Rockafellar duality theorem: Lagrange multiplier theorems and hyperplane theorems for convex optimization and best approximation
• Minimization of continuous convex functional on complements of convex subsets of locally convex spaces¹

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