Some criteria for maximal abstract monotonicity
type: Item
instance of: scholarly article
title: Some criteria for maximal abstract monotonicity
zbMATH Open document ID: 1262.47076
published in: Journal of Global Optimization
publication date: 2012-10-01T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/182652
review text: The authors develop a theory of monotone operators in the framework of abstract convexity. They prove a Rockafellar type surjectivity result and then, by using an additivity constraint qualification, they obtain a generalization of the Fenchel duality theorem. Criteria for maximal abstract monotonicity as well as necessary and sufficient conditions for maximality of abstract monotone operators are also presented.
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 6088795
zbMATH Keywords: constraint qualification
zbMATH Keywords: generalized Fenchel's duality
zbMATH Keywords: monotone operator
zbMATH Keywords: abstract monotonicity
zbMATH Keywords: abstract convex function
zbMATH Keywords: abstract convexity
Wikidata QID: Q57836324
author: H. Mohebi
author: Juan-Enrique Martínez-Legaz
author: Marco Rocco
reviewed by: Rodica Luca
MaRDI profile type: Publication
OpenAlex ID: W2041239292
cites work: Q3509482
cites work: Maximal monotone operators, convex functions and a special family of enlargements
cites work: Maximal monotonicity, conjugation and the duality product
cites work: Techniques of variational analysis
cites work: Maximal abstract monotonicity and generalized Fenchel's conjugation formulas
cites work: Generalized Fenchel's conjugation formulas and duality for abstract convex functions
cites work: Q3732408
cites work: Abstract convexity in measure theory and in convex analysis.
cites work: Abstract cyclical monotonicity and Monge solutions for the general Monge-Kantorovich problem
cites work: Q3632466
cites work: Fenchel duality and related properties in generalized conjugation theory
cites work: Monotone operators representable by l.s.c. convex functions
cites work: Q3066282
cites work: Monotonic analysis over ordered topological vector spaces: I
cites work: Inf-convolution, sous-additivite, convexite des fonctions numériques
cites work: Q3126366
cites work: The relevance of convex analysis for the study of monotonicity
cites work: Autoconjugate functions and representations of monotone operators
cites work: Q2997138
cites work: Abstract convexity and global optimization
cites work: Minimizing increasing star-shaped functions based on abstract convexity
cites work: Increasing convex-along-rays functions with applications to global optimization
cites work: On global optimality conditions via separation functions
cites work: Convex-along-rays functions and star-shaped sets
cites work: Q4681452
cites work: Q4339231
cites work: Minimax monotonicity
cites work: Q4681438
DBLP publication ID: journals/jgo/MohebiMR12
DOI: 10.1007/S10898-011-9671-8
description: scientific article; zbMATH DE number 6088795