Direct theorems in semi-infinite convex programming

DOI10.1007/BF01584251zbMath0469.90065OpenAlexW2048093585WikidataQ56936028 ScholiaQ56936028MaRDI QIDQ3923950

Jonathan M. Borwein

Publication date: 1981

Published in: Mathematical Programming (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01584251

zbMATH Keywords

dualityHelly-type theoremdirect theoremmulticriteria programmingquasi-differentiable programmingabstract programmingexistence of finite subprogramsfinitely many variablesinfinitely constrained programming problemssemi-infinite quasi-convex program

Mathematics Subject Classification ID

Convex programming (90C25) Sensitivity, stability, parametric optimization (90C31) Programming in abstract spaces (90C48) Duality theory (optimization) (49N15)

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Cites Work

• Affine minorants minimizing the sum of convex functions
• Helly's theorem and minima of convex functions
• Proper efficiency and the theory of vector maximization
• Duality in Semi-Infinite Programs and Some Works of Haar and Carathéodory
• DUALITY, HAAR PROGRAMS, AND FINITE SEQUENCE SPACES
• Characterizations of optimality without constraint qualification for the abstract convex program
• Proper Efficient Points for Maximizations with Respect to Cones
• An Infinite Linear Program with a Duality Gap
• On Representations of Semi-Infinite Programs which Have No Duality Gaps
• Seven Kinds of Convexity
• Convex Analysis
• Quasi-Convex Programming
• The Critical Set of a Convex Body
• Sufficient conditions for extremum, penalty functions and regularity
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