Generalized Fenchel's conjugation formulas and duality for abstract convex functions

DOI10.1007/s10957-007-9185-1zbMath1146.49013OpenAlexW2137493863MaRDI QIDQ946326

Alexander Rubinov, Vaithilingam Jeyakumar, Zhi-You Wu

Publication date: 23 September 2008

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-007-9185-1

zbMATH Keywords

generalized Fenchel's dualityabstract convexity of sets and functionsglobal nonaffine supportsinfimal convolutions

Mathematics Subject Classification ID

Convex programming (90C25) Set-valued and variational analysis (49J53) Convex functions and convex programs in convex geometry (52A41) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (14)

Note on Convex Functionals in the Dual Spaces of Nonreflexive Banach Spaces ⋮ Duality for composite optimization problem within the framework of abstract convexity ⋮ Global optimization of the difference of two increasing plus-convex-along-rays functions ⋮ Zero duality gap conditions via abstract convexity ⋮ On duality for nonconvex minimization problems within the framework of abstract convexity ⋮ Characterizing approximate global minimizers of the difference of two abstract convex functions with applications ⋮ Generalized positive sets and abstract monotonicity ⋮ Vector topical function, abstract convexity and image space analysis ⋮ Necessary and sufficient constraint qualification for surrogate duality ⋮ Some criteria for maximal abstract monotonicity ⋮ Global optimality conditions for some classes of optimization problems ⋮ Maximal abstract monotonicity and generalized Fenchel's conjugation formulas ⋮ Infimal convolution and duality in problems with third-order discrete and differential inclusions ⋮ Adaptive global algorithm for solving box-constrained non-convex quadratic minimization problems

Cites Work

• Inf-convolution, sous-additivite, convexite des fonctions numériques
• A new geometric condition for Fenchel's duality in infinite dimensional spaces
• A simple closure condition for the normal cone intersection formula
• Abstract convexity and global optimization
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