SIAM journal on optimization, ISSN 1095-7189, 2011, Volume 21, Issue 4, pp. 1230 - 1250

...SIAM J. OPTIM. c Vol. 21, No. 4, pp. 12301250 A MONOTONE + SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY LUIS M. BRICE NO-ARIAS AND PATRICK...

Monotone inclusion | Minimization algorithm | Convex optimization | Composite operator | Operator splitting | Decomposition | Duality | Fenchel-Rockafellar duality | Monotone operator | Forward-backward-forward algorithm | Mathematics | Optimization and Control

Monotone inclusion | Minimization algorithm | Convex optimization | Composite operator | Operator splitting | Decomposition | Duality | Fenchel-Rockafellar duality | Monotone operator | Forward-backward-forward algorithm | Mathematics | Optimization and Control

Journal Article

Journal of approximation theory, ISSN 0021-9045, 2012, Volume 164, Issue 8, pp. 1065 - 1084

.... In this paper, we systematically study Attouch–Théra duality for this problem. We provide new results related...

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 9/2015, Volume 46, Issue 3, pp. 353 - 389

...) / 1678-7714 (Online) Entropy , Pressure and Duality for Gibbs plans in Ergodic Transport A.O. Lopes*, J.K. Mengue, J. Mohr and R.R. Souza Abstract. Let X be a nite set...

Kantorovich Duality | Theoretical, Mathematical and Computational Physics | Mathematics | 37D35 | pressure | ergodic transport | 90B06 | Gibbs plans | Thermodynamic Formalism | Ruelle Operator | subaction | entropy | 37C30 | zero temperature | 37A35 | Mathematics, general | Fenchel-Rockafellar duality | 37A60 | ZERO-TEMPERATURE | MATHEMATICS | SETS | Thermodynamics

Kantorovich Duality | Theoretical, Mathematical and Computational Physics | Mathematics | 37D35 | pressure | ergodic transport | 90B06 | Gibbs plans | Thermodynamic Formalism | Ruelle Operator | subaction | entropy | 37C30 | zero temperature | 37A35 | Mathematics, general | Fenchel-Rockafellar duality | 37A60 | ZERO-TEMPERATURE | MATHEMATICS | SETS | Thermodynamics

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2012, Volume 158, Issue 2, pp. 460 - 479

We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the...

Monotone inclusion | Mathematics | Theory of Computation | Optimization | Primal–dual algorithm | Douglas–Rachford method | Proximal method | Fenchel–Rockafellar duality | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Forward–backward method | Operator splitting | Applications of Mathematics | Engineering, general | Convex and nonsmooth optimization | Douglas-Rachford method | Primal-dual algorithm | Fenchel-Rockafellar duality | Forward-backward method | MATHEMATICS, APPLIED | DECOMPOSITION | SUM | ALGORITHMS | RECOVERY | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Convex analysis | Formulations | Operators | Splitting | Composite functions | Inversions | Linear operators | Optimization and Control | Engineering Sciences | Signal and Image processing

Monotone inclusion | Mathematics | Theory of Computation | Optimization | Primal–dual algorithm | Douglas–Rachford method | Proximal method | Fenchel–Rockafellar duality | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Forward–backward method | Operator splitting | Applications of Mathematics | Engineering, general | Convex and nonsmooth optimization | Douglas-Rachford method | Primal-dual algorithm | Fenchel-Rockafellar duality | Forward-backward method | MATHEMATICS, APPLIED | DECOMPOSITION | SUM | ALGORITHMS | RECOVERY | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Analysis | Methods | Algorithms | Studies | Convex analysis | Formulations | Operators | Splitting | Composite functions | Inversions | Linear operators | Optimization and Control | Engineering Sciences | Signal and Image processing

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 13, pp. 4550 - 4572

We show that the set of fixed points of the average of two resolvents can be found from the set of fixed points for compositions of two resolvents associated...

Strongly nonexpansive mapping | Proximal average | Resolvent composition | Moreau envelope | Resolvent average | Projection | Proximal mapping | Monotone operator | Yosida regularization | Proximal point method | Fenchel–Rockafellar duality | Firmly nonexpansive mapping | Convex function | Hilbert space | Attouch–Théra duality | Fixed point | FenchelRockafellar duality | AttouchThra duality | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | Attouch-Thera duality | ALGORITHM | MATHEMATICS | CONVEX | Fenchel-Rockafellar duality | HILBERT-SPACE | MONOTONE-OPERATORS | Operators | Least squares method | Nonlinearity | Mapping | Indicators | Constraining | Fixed points (mathematics)

Strongly nonexpansive mapping | Proximal average | Resolvent composition | Moreau envelope | Resolvent average | Projection | Proximal mapping | Monotone operator | Yosida regularization | Proximal point method | Fenchel–Rockafellar duality | Firmly nonexpansive mapping | Convex function | Hilbert space | Attouch–Théra duality | Fixed point | FenchelRockafellar duality | AttouchThra duality | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | Attouch-Thera duality | ALGORITHM | MATHEMATICS | CONVEX | Fenchel-Rockafellar duality | HILBERT-SPACE | MONOTONE-OPERATORS | Operators | Least squares method | Nonlinearity | Mapping | Indicators | Constraining | Fixed points (mathematics)

Journal Article

SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2011, Volume 21, Issue 4, pp. 1230 - 1250

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and...

MATHEMATICS, APPLIED | forward-backward-forward algorithm | SIGNAL RECOVERY | decomposition | PROXIMAL POINT ALGORITHM | SUM | minimization algorithm | duality | monotone operator | VARIATIONAL-INEQUALITIES | convex optimization | MAPPINGS | CONVERGENCE | DUALIZATION | Fenchel-Rockafellar duality | composite operator | operator splitting | OPERATORS | monotone inclusion

MATHEMATICS, APPLIED | forward-backward-forward algorithm | SIGNAL RECOVERY | decomposition | PROXIMAL POINT ALGORITHM | SUM | minimization algorithm | duality | monotone operator | VARIATIONAL-INEQUALITIES | convex optimization | MAPPINGS | CONVERGENCE | DUALIZATION | Fenchel-Rockafellar duality | composite operator | operator splitting | OPERATORS | monotone inclusion

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2017, Volume 27, Issue 4, pp. 2459 - 2480

The paper deals with some theoretical and numerical aspects for an optimal matching problem with constraints. It is known that the uniqueness of the optimal...

Augmented Lagrangian methods | Fenchel–Rockafellar duality | Optimal matching | Optimal transport | MATHEMATICS, APPLIED | optimal matching | optimal transport | Fenchel-Rockafellar duality | augmented Lagrangian methods | Mathematics | Optimization and Control | Analysis of PDEs | Numerical Analysis

Augmented Lagrangian methods | Fenchel–Rockafellar duality | Optimal matching | Optimal transport | MATHEMATICS, APPLIED | optimal matching | optimal transport | Fenchel-Rockafellar duality | augmented Lagrangian methods | Mathematics | Optimization and Control | Analysis of PDEs | Numerical Analysis

Journal Article

Optimization, ISSN 0233-1934, 02/2015, Volume 64, Issue 2, pp. 197 - 223

.... To the set-valued conjugate, a full calculus is provided, including a biconjugation theorem, a chain rule and weak and strong duality results of the Fenchel-Rockafellar...

biconjugation theorem | set-valued function | Fenchel-Rockafellar duality | Legendre-Fenchel conjugate | Fenchel–Rockafellar duality | Legendre–Fenchel conjugate | MATHEMATICS, APPLIED | RISK | CONVEX-SETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C46 | DUALITY | CONVERGENCE | 49N15 | OPTIMIZATION | 54C60 | Conjugates | Mathematical analysis | Chains | Scalars | Calculus | Conjugation | Representations | Optimization | Mathematics - Optimization and Control

biconjugation theorem | set-valued function | Fenchel-Rockafellar duality | Legendre-Fenchel conjugate | Fenchel–Rockafellar duality | Legendre–Fenchel conjugate | MATHEMATICS, APPLIED | RISK | CONVEX-SETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C46 | DUALITY | CONVERGENCE | 49N15 | OPTIMIZATION | 54C60 | Conjugates | Mathematical analysis | Chains | Scalars | Calculus | Conjugation | Representations | Optimization | Mathematics - Optimization and Control

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 2018, Volume 52, Issue 5, pp. 2109 - 2132

We introduce a dual dynamical formulation for the optimal partial transport problem with Lagrangian costs C-L(x, y) := inf (xi)(is an element of...

Augmented Lagrangian method | Optimal partial transport | Fenchel-Rockafellar duality | Optimal transport | MATHEMATICS, APPLIED | augmented Lagrangian method | REGULARITY | DENSITY CONSTRAINTS | FREE-BOUNDARY | MEAN-FIELD GAMES | VARIATIONAL FORMULATION | optimal partial transport | Formulations | Lagrange multiplier | Approximation | Mathematical analysis | Optimization

Augmented Lagrangian method | Optimal partial transport | Fenchel-Rockafellar duality | Optimal transport | MATHEMATICS, APPLIED | augmented Lagrangian method | REGULARITY | DENSITY CONSTRAINTS | FREE-BOUNDARY | MEAN-FIELD GAMES | VARIATIONAL FORMULATION | optimal partial transport | Formulations | Lagrange multiplier | Approximation | Mathematical analysis | Optimization

Journal Article

Optimization: VIII Brazilian Workshop on Continuous Optimization dedicated to Professor Alfredo Iusem on the occasion of his 60th birthday, Mambucaba, Rio de Janeiro, Brazil, July 13-17, 2009 - Guest Eds: Regina Burachik and Jinyun Yuan, ISSN 0233-1934, 08/2011, Volume 60, Issue 8-9, pp. 1023 - 1043

A duality theorem of the Fenchel-Rockafellar type for set-valued optimization problems is presented along with a result for the conjugate of the sum of two set-valued functions and a chain rule...

Fenchel-Rockafellar theorem | set relations | conlinear space | supremal convolution | set-valued function | Fenchel conjugate | duality | set-valued risk measures | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | Functions (mathematics) | Conjugates | Duality theorem | Mathematical analysis | Finance | Mathematical models | Linear operators | Optimization

Fenchel-Rockafellar theorem | set relations | conlinear space | supremal convolution | set-valued function | Fenchel conjugate | duality | set-valued risk measures | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | Functions (mathematics) | Conjugates | Duality theorem | Mathematical analysis | Finance | Mathematical models | Linear operators | Optimization

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 7/2019, pp. 1 - 1

Barcode encoding schemes impose symbolic constraints which fix certain segments of the image. We present, implement, and assess a method for blind deblurring...

maximum entropy on the mean | Noise reduction | Estimation | UPC barcode | Entropy | Probability distribution | QR barcode | Kullback-Leibler divergence | blind deblurring | denoising | symbology | L-BFGS | Cameras | Fenchel-Rockafellar duality | Kernel

maximum entropy on the mean | Noise reduction | Estimation | UPC barcode | Entropy | Probability distribution | QR barcode | Kullback-Leibler divergence | blind deblurring | denoising | symbology | L-BFGS | Cameras | Fenchel-Rockafellar duality | Kernel

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2007, Volume 46, Issue 6, pp. 2256 - 2279

.... The proof combines the Fenchel-Rockafellar duality theory and a fixed point argument. When the control is restricted to be active in a proper open subset of the whole...

Obstruction phenomenon | Fenchel-Rockafellar duality theory | Newtonian filtration equation | Approximate controllability | EXISTENCE | approximate controllability | MATHEMATICS, APPLIED | NULL CONTROLLABILITY | PARABOLIC EQUATIONS | HEAT-EQUATION | obstruction phenomenon | SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Obstruction phenomenon | Fenchel-Rockafellar duality theory | Newtonian filtration equation | Approximate controllability | EXISTENCE | approximate controllability | MATHEMATICS, APPLIED | NULL CONTROLLABILITY | PARABOLIC EQUATIONS | HEAT-EQUATION | obstruction phenomenon | SYSTEMS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Cette thèse est consacrée à l'analyse mathématique et numérique pour les problèmes de transport partiel optimal et d'appariement avec contrainte (constrained...

Problème d'appariement optimal | Dualité de Fenchel--Rockafellar | Transport partiel optimal | Méthodes du lagrangien augmenté | 519.7 | Équation de Monge--Kantorovich | Transport optimal | Optimal transport | Optimal partial transport | Doublant des variables | Fenchel--Rockafellar duality | Monge--Kantorovich equation | Optimal matching | Augmented lagrangian methods | Doubling variables

Problème d'appariement optimal | Dualité de Fenchel--Rockafellar | Transport partiel optimal | Méthodes du lagrangien augmenté | 519.7 | Équation de Monge--Kantorovich | Transport optimal | Optimal transport | Optimal partial transport | Doublant des variables | Fenchel--Rockafellar duality | Monge--Kantorovich equation | Optimal matching | Augmented lagrangian methods | Doubling variables

Dissertation

Set-Valued Analysis, ISSN 0927-6947, 9/2007, Volume 15, Issue 3, pp. 297 - 306

.... It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.

Geometry | Fenchel–Rockafellar duality | Primary 47H05 | Secondary 90C25 | Analysis | Mathematics | convex analysis | Debrunner–Flor extension | Fitzpatrick functions | cyclic monotonicity | monotone operator | Cyclic monotonicity | Debrunner-Flor extension | Fenchel-Rockafellar duality | Monotone operator | Convex analysis | MATHEMATICS, APPLIED | FENCHEL DUALITY

Geometry | Fenchel–Rockafellar duality | Primary 47H05 | Secondary 90C25 | Analysis | Mathematics | convex analysis | Debrunner–Flor extension | Fitzpatrick functions | cyclic monotonicity | monotone operator | Cyclic monotonicity | Debrunner-Flor extension | Fenchel-Rockafellar duality | Monotone operator | Convex analysis | MATHEMATICS, APPLIED | FENCHEL DUALITY

Journal Article

12/1998, ISBN 9780471252894, 59

... of Convex and Concave Functions Fenchel Duality Theorem Rockafellar Duality Theorem Proof of Lemma C Norms, Dual Norms, Minkowski Norms Generalized Fermat...

Fenchel duality theorem | Fenchel‐Rockafellar duality theory | convex function | hyperplane | epigraph

Fenchel duality theorem | Fenchel‐Rockafellar duality theory | convex function | hyperplane | epigraph

Book Chapter

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2015, Volume 166, Issue 3, pp. 861 - 888

Many inverse problems can be formulated as split feasibility problems. To find feasible solutions, one has to minimize proximity functions. We show that the...

Fenchel–Rockafellar’s duality | CQ$$ C Q -algorithm | Mathematics | Theory of Computation | Split feasibility problem | Proximal point method | Optimization | 47H10 | 90C30 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 65K10 | Applications of Mathematics | Engineering, general | Proximity function | 47H04 | CQ-algorithm | MATHEMATICS, APPLIED | SIGNAL RECOVERY | ALGORITHM | CONVEX-SETS | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Fenchel-Rockafellar's duality | Censorship | Algorithms | Studies | Optimization algorithms | Feasibility | Hilbert space | Mathematical analysis | Proximity | Inverse problems | Equivalence | Projection | Mathematical models

Fenchel–Rockafellar’s duality | CQ$$ C Q -algorithm | Mathematics | Theory of Computation | Split feasibility problem | Proximal point method | Optimization | 47H10 | 90C30 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 65K10 | Applications of Mathematics | Engineering, general | Proximity function | 47H04 | CQ-algorithm | MATHEMATICS, APPLIED | SIGNAL RECOVERY | ALGORITHM | CONVEX-SETS | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Fenchel-Rockafellar's duality | Censorship | Algorithms | Studies | Optimization algorithms | Feasibility | Hilbert space | Mathematical analysis | Proximity | Inverse problems | Equivalence | Projection | Mathematical models

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 11/1984, Volume 9, Issue 4, pp. 576 - 591

.... A comparable theorem is given for semicontinuous quasi-saddle functions. The new criterion is applied to constrained saddlepoint problems and to the Fenchel-Rockafellar duality model for constrained convex minimization...

saddle functions | minimax criteria | Knaster-Kuratowski-Mazurkiewicz lemma | abstract spaces | minimax solutions | minimaximizing sequences | Fenchel-Rockafellar duality model | Ky Fan lemma | quasi-saddle functions | Minimax | Mathematical theorems | Logical theorems | Economic theory | Topological vector spaces | Mathematical functions | Mathematics | Mathematical duality | Convexity | Minimax problems | Usage | Analysis | Geometry, Differential | Functions | Topology | Vector spaces | Research

saddle functions | minimax criteria | Knaster-Kuratowski-Mazurkiewicz lemma | abstract spaces | minimax solutions | minimaximizing sequences | Fenchel-Rockafellar duality model | Ky Fan lemma | quasi-saddle functions | Minimax | Mathematical theorems | Logical theorems | Economic theory | Topological vector spaces | Mathematical functions | Mathematics | Mathematical duality | Convexity | Minimax problems | Usage | Analysis | Geometry, Differential | Functions | Topology | Vector spaces | Research

Journal Article

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