Maximal Monotonicity and Cyclic Involutivity of Multiconjugate Convex Functions

DOI10.1137/23m1549201arXiv2207.04830OpenAlexW4387501365MaRDI QIDQ6076856

Tongseok Lim

Publication date: 17 October 2023

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04830

zbMATH Keywords

maximal monotonicitymultimarginal optimal transport\(c\)-monotonicity\(c\)-convex conjugacycyclical involutivitymultivariate convex analysis

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Axiomatic and generalized convexity (52A01) Duality theory (optimization) (49N15) Convexity of real functions of several variables, generalizations (26B25) Matching models (91B68) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Cites Work

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• Symmetric Monge-Kantorovich problems and polar decompositions of vector fields
• Wasserstein barycenters over Riemannian manifolds
• Hidden structures in the class of convex functions and a new duality transform
• On the local structure of optimal measures in the multi-marginal optimal transportation problem
• A characterization of the duality mapping for convex bodies
• Conjugate duality in convex optimization
• On the optimal mapping of distributions
• Duality for nonconvex optimization and its applications
• A convexity principle for interacting gases
• The geometry of optimal transportation
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Monotone operator theory in convex optimization
• A class of multi-marginal \(c\)-cyclically monotone sets with explicit \(c\)-splitting potentials
• Multi-marginal maximal monotonicity and convex analysis
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• On the maximal monotonicity of subdifferential mappings
• Multi-marginal optimal transport on Riemannian manifolds
• Barycenters in the Wasserstein Space
• Duality theorems for marginal problems
• Multi-marginal optimal transport: Theory and applications
• Polar factorization and monotone rearrangement of vector‐valued functions
• Optimal maps for the multidimensional Monge-Kantorovich problem
• Variational Analysis
• Density Functional Theory and Optimal Transportation with Coulomb Cost
• Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs
• Multi-Marginal Optimal Transportation Problem for Cyclic Costs
• Large-Scale Convex Optimization
• A General Condition for Monge Solutions in the Multi-Marginal Optimal Transport Problem
• Convex Analysis
• The Resolvent Order: A Unification of the Orders by Zarantonello, by Loewner, and by Moreau
• Convex analysis and monotone operator theory in Hilbert spaces
• Optimal Transport
• A zoo of dualities

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