Journal of Functional Analysis, ISSN 0022-1236, 06/2019, Volume 276, Issue 11, pp. 3304 - 3324

The Monge-Kantorovich problem for the W∞ distance presents several peculiarities. Among them the lack of convexity and then of a direct duality. We study in...

Monge-Kantorovich problem | Cyclical monotonicity | Optimal transport problem

Monge-Kantorovich problem | Cyclical monotonicity | Optimal transport problem

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2019, Volume 277, Issue 6, pp. 1581 - 1602

We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the...

Monotonicity formula | Free boundary problems | Elliptic equations | MATHEMATICS

Monotonicity formula | Free boundary problems | Elliptic equations | MATHEMATICS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2019, Volume 77, Issue 11, pp. 2989 - 3000

We consider an abstract system with Lagrange multipliers which consists of a hemivariational inequality and a variational inequality. The hemivariational...

Nonlinearity | Contact problems | Hemicontinuity | Generalized monotonicity | Weak solutions | Hemivariational–variational problem with Lagrange multipliers | MATHEMATICS, APPLIED | APPROXIMATION | Hemivariational-variational problem with Lagrange multipliers | COULOMB-FRICTION | Boundary value problems | Banach space | Lagrange multipliers | Portfolio management | Inequality

Nonlinearity | Contact problems | Hemicontinuity | Generalized monotonicity | Weak solutions | Hemivariational–variational problem with Lagrange multipliers | MATHEMATICS, APPLIED | APPROXIMATION | Hemivariational-variational problem with Lagrange multipliers | COULOMB-FRICTION | Boundary value problems | Banach space | Lagrange multipliers | Portfolio management | Inequality

Journal Article

4.
Full Text
Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem

Journal of Optimization Theory and Applications, ISSN 0022-3239, 6/2007, Volume 133, Issue 3, pp. 359 - 370

In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions...

Firmly nonexpansive mappings | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Weak and strong convergence | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Nonexpansive mappings | Monotonicity | equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | firmly nonexpansive mappings | weak and strong convergence | monotonicity | nonexpansive mappings | Studies | Mathematical models | Equilibrium | Convergence | Theorems | Hilbert space | Mapping

Firmly nonexpansive mappings | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Weak and strong convergence | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Nonexpansive mappings | Monotonicity | equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | firmly nonexpansive mappings | weak and strong convergence | monotonicity | nonexpansive mappings | Studies | Mathematical models | Equilibrium | Convergence | Theorems | Hilbert space | Mapping

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 12, pp. 4083 - 4087

Based on the very recent work by Censor and Segal (2009) [1], and inspired by Xu (2006) [9], Zhao and Yang (2005) [10], and Bauschke and Combettes (2001) ...

Fejér monotonicity | Feasibility problem | Quasi-nonexpansive operator | Fejr monotonicity | MATHEMATICS | PROJECTION | MATHEMATICS, APPLIED | SET | Fejer monotonicity | Analysis | Algorithms | Nonlinearity | Operators | Fixed points (mathematics) | Feasibility | Hilbert space | Mathematics | Optimization and Control

Fejér monotonicity | Feasibility problem | Quasi-nonexpansive operator | Fejr monotonicity | MATHEMATICS | PROJECTION | MATHEMATICS, APPLIED | SET | Fejer monotonicity | Analysis | Algorithms | Nonlinearity | Operators | Fixed points (mathematics) | Feasibility | Hilbert space | Mathematics | Optimization and Control

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 6, pp. 4559 - 4605

Given s, sigma is an element of (0, 1) and a bounded domain Omega subset of R-n, we consider the following minimization problem of...

Fractional perimeter | Classification of cones | Monotonicity formula | Minimization problem | MATHEMATICS, APPLIED | MINIMAL-SURFACES | monotonicity formula | CALCULUS | classification of cones | EQUATIONS | fractional perimeter | LAPLACIAN | MINIMIZATION | REGULARITY | minimization problem | FRACTIONAL SOBOLEV SPACES | PERIMETER

Fractional perimeter | Classification of cones | Monotonicity formula | Minimization problem | MATHEMATICS, APPLIED | MINIMAL-SURFACES | monotonicity formula | CALCULUS | classification of cones | EQUATIONS | fractional perimeter | LAPLACIAN | MINIMIZATION | REGULARITY | minimization problem | FRACTIONAL SOBOLEV SPACES | PERIMETER

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 9/2008, Volume 12, Issue 6, pp. 1401 - 1432

In this paper, we introduce a new iterative scheme based on the hybrid method and the extragradient method for finding a common element of the set of solutions...

Mathematical theorems | Mathematical monotonicity | Approximation | Applied mathematics | Hilbert spaces | Nash equilibrium | Mathematical inequalities | Banach space | Perceptron convergence procedure | Variational inequalities | Strong convergence | Hybrid method | Monotone mapping | Variational inequality | Extragradient method | Generalized mixed equilibrium problem | Nonexpansive mapping | Fixed point | monotone mapping | APPROXIMATION METHODS | HILBERT-SPACES | NONEXPANSIVE-MAPPINGS | hybrid method | ITERATIVE METHOD | nonexpansive mapping | variational inequality | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | ALGORITHMS | generalized mixed equilibrium problem | strong convergence | WEAK | MATHEMATICS | extragradient method | fixed point | BANACH-SPACES | CONSTRUCTION

Mathematical theorems | Mathematical monotonicity | Approximation | Applied mathematics | Hilbert spaces | Nash equilibrium | Mathematical inequalities | Banach space | Perceptron convergence procedure | Variational inequalities | Strong convergence | Hybrid method | Monotone mapping | Variational inequality | Extragradient method | Generalized mixed equilibrium problem | Nonexpansive mapping | Fixed point | monotone mapping | APPROXIMATION METHODS | HILBERT-SPACES | NONEXPANSIVE-MAPPINGS | hybrid method | ITERATIVE METHOD | nonexpansive mapping | variational inequality | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | ALGORITHMS | generalized mixed equilibrium problem | strong convergence | WEAK | MATHEMATICS | extragradient method | fixed point | BANACH-SPACES | CONSTRUCTION

Journal Article

Inverse Problems, ISSN 0266-5611, 01/2019, Volume 35, Issue 3, p. 34001

This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter tau >= 0. The...

p-Laplacian | Bayesian inversion | inverse boundary value problem | linearization | MATHEMATICS, APPLIED | APPROXIMATION | RECONSTRUCTION | MONOTONICITY | PHYSICS, MATHEMATICAL | HARMONIC FUNCTIONS | REGULARITY | IMPEDANCE TOMOGRAPHY | EQUATION

p-Laplacian | Bayesian inversion | inverse boundary value problem | linearization | MATHEMATICS, APPLIED | APPROXIMATION | RECONSTRUCTION | MONOTONICITY | PHYSICS, MATHEMATICAL | HARMONIC FUNCTIONS | REGULARITY | IMPEDANCE TOMOGRAPHY | EQUATION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2018, Volume 146, Issue 11, pp. 4735 - 4740

This paper establishes that a generalization of c-cyclical monotonicity from the Monge-Kantorovich problem with two marginals gives rise to a sufficient...

Mass transport | Cyclical monotonicity | PLANS | MATHEMATICS | MATHEMATICS, APPLIED | mass transport | CONSTRAINTS | OPTIMAL TRANSPORT

Mass transport | Cyclical monotonicity | PLANS | MATHEMATICS | MATHEMATICS, APPLIED | mass transport | CONSTRAINTS | OPTIMAL TRANSPORT

Journal Article

Journal of Statistical Planning and Inference, ISSN 0378-3758, 03/2020, Volume 205, pp. 203 - 218

We study the problem of detecting as quickly as possible the disorder time at which a purely jump Lévy process changes its probabilistic features. Assuming...

Disorder problem | Optimal stopping | Lévy processes | Complete monotonicity | Hyperexponential processes | SEQUENTIAL DETECTION | Levy processes | CONVERGENCE | STATISTICS & PROBABILITY | QUICKEST DETECTION PROBLEMS | EXPONENTIAL PENALTY

Disorder problem | Optimal stopping | Lévy processes | Complete monotonicity | Hyperexponential processes | SEQUENTIAL DETECTION | Levy processes | CONVERGENCE | STATISTICS & PROBABILITY | QUICKEST DETECTION PROBLEMS | EXPONENTIAL PENALTY

Journal Article

INVERSE PROBLEMS, ISSN 0266-5611, 02/2019, Volume 35, Issue 2, p. 24005

For the linearized reconstruction problem in electrical impedance tomography with the complete electrode model, Lechleiter and Rieder (2008 Inverse Problems 24...

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | Lipschitz stability | complete electrode model (CEM) | GLOBAL UNIQUENESS | monotonicity | electrical impedance tomography (EIT) | MODEL | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | localized potentials | COEFFICIENT | uniqueness | INVERSE CONDUCTIVITY PROBLEM | SHAPE-RECONSTRUCTION

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | Lipschitz stability | complete electrode model (CEM) | GLOBAL UNIQUENESS | monotonicity | electrical impedance tomography (EIT) | MODEL | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | localized potentials | COEFFICIENT | uniqueness | INVERSE CONDUCTIVITY PROBLEM | SHAPE-RECONSTRUCTION

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 16

The purpose of this paper is to focus on the well-posedness for a generalized (η,g,φ) $(\eta ,g,\varphi )$-mixed vector variational-type inequality and...

Relaxed η - α g $\alpha _{g}$ - P -monotonicity | Mathematics | 54H25 | Generalized ( η , g , φ ) $(\eta ,g,\varphi )$ -mixed vector variational-type inequality problems | 47J20 | 49K40 | Analysis | 90C33 | 47H09 | Mathematics, general | Applications of Mathematics | 54C60 | Optimization problems | Well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | Relaxed eta-alpha(g)-P-monotonicity | Generalized (eta,g,phi)-mixed vector variational-type inequality problems | EQUILIBRIUM PROBLEMS | INCLUSION PROBLEMS | Economic models | Well posed problems | Optimization | Inequality | Relaxed η- α g $\alpha _{g}$ -P-monotonicity

Relaxed η - α g $\alpha _{g}$ - P -monotonicity | Mathematics | 54H25 | Generalized ( η , g , φ ) $(\eta ,g,\varphi )$ -mixed vector variational-type inequality problems | 47J20 | 49K40 | Analysis | 90C33 | 47H09 | Mathematics, general | Applications of Mathematics | 54C60 | Optimization problems | Well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | Relaxed eta-alpha(g)-P-monotonicity | Generalized (eta,g,phi)-mixed vector variational-type inequality problems | EQUILIBRIUM PROBLEMS | INCLUSION PROBLEMS | Economic models | Well posed problems | Optimization | Inequality | Relaxed η- α g $\alpha _{g}$ -P-monotonicity

Journal Article

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, ISSN 0956-7925, 12/2019, Volume 30, Issue 6, pp. 1210 - 1219

It is proved that c-cyclical monotonicity is a sufficient condition for optimality in the multi-marginal optimal transport problem with Coulomb repulsive cost....

MATHEMATICS, APPLIED | MONGE SOLUTIONS | c-cyclical monotonicity | Multi-marginal optimal transportation | Monge-Kantorovich problem | optimality condition | Transport | Optimization

MATHEMATICS, APPLIED | MONGE SOLUTIONS | c-cyclical monotonicity | Multi-marginal optimal transportation | Monge-Kantorovich problem | optimality condition | Transport | Optimization

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2019, Volume 25, Issue 6, pp. 3310 - 3341

Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz...

Mathematics | Boas conjecture | Abstract Harmonic Analysis | Hankel transform | Mathematical Methods in Physics | Fourier Analysis | Secondary 26A48 | Signal,Image and Speech Processing | Lorentz spaces | Approximations and Expansions | General monotonicity | Partial Differential Equations | 26D15 | Weighted Lebesgue spaces | Primary 42A38 | MATHEMATICS, APPLIED | INTEGRABILITY | NORM INEQUALITIES | SMOOTHNESS | THEOREM | SPACES | WEIGHTED FOURIER INEQUALITIES | TRIGONOMETRIC SERIES | CONJECTURE | INTERPOLATION

Mathematics | Boas conjecture | Abstract Harmonic Analysis | Hankel transform | Mathematical Methods in Physics | Fourier Analysis | Secondary 26A48 | Signal,Image and Speech Processing | Lorentz spaces | Approximations and Expansions | General monotonicity | Partial Differential Equations | 26D15 | Weighted Lebesgue spaces | Primary 42A38 | MATHEMATICS, APPLIED | INTEGRABILITY | NORM INEQUALITIES | SMOOTHNESS | THEOREM | SPACES | WEIGHTED FOURIER INEQUALITIES | TRIGONOMETRIC SERIES | CONJECTURE | INTERPOLATION

Journal Article

Comptes Rendus Mathematique, ISSN 1631-073X, 02/2018, Volume 356, Issue 2, pp. 207 - 213

In Optimal Transport theory, three quantities play a central role: the minimal cost of transport, originally introduced by Monge, its relaxed version...

MATHEMATICS | MONOTONICITY | CONNECTIONS | OPTIMAL TRANSPORTATION

MATHEMATICS | MONOTONICITY | CONNECTIONS | OPTIMAL TRANSPORTATION

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 3, pp. 1879 - 1905

We study minimizers of the functional integral(+)(B1) vertical bar del u vertical bar(2)x(n)(a) dx + 2 integral(')(B1)(lambda + u(+) + lambda-u(-)) dx' for a...

Two-phase free boundary problem | Alt-Caffarelli-Friedman monotoncity formula | Separation of phases | Fractional obstacle problem | Fractional Laplacian | Thin obstacle problem | Weiss-type monotonicity formula | Almgen's frequency formula | MATHEMATICS, APPLIED | REGULARITY | two-phase free boundary problem | fractional Laplacian | FREE-BOUNDARY | separation of phases | fractional obstacle problem | thin obstacle problem

Two-phase free boundary problem | Alt-Caffarelli-Friedman monotoncity formula | Separation of phases | Fractional obstacle problem | Fractional Laplacian | Thin obstacle problem | Weiss-type monotonicity formula | Almgen's frequency formula | MATHEMATICS, APPLIED | REGULARITY | two-phase free boundary problem | fractional Laplacian | FREE-BOUNDARY | separation of phases | fractional obstacle problem | thin obstacle problem

Journal Article

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Linear convergence of the generalized Douglas–Rachford algorithm for feasibility problems

Journal of Global Optimization, ISSN 0925-5001, 11/2018, Volume 72, Issue 3, pp. 443 - 474

In this paper, we study the generalized Douglas–Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical...

Quasi coercivity | 65K05 | Mathematics | 90C26 | Optimization | Quasi Fejér monotonicity | Cyclic algorithm | Linear convergence | Linear regularity | Superregularity | Operations Research/Decision Theory | 65K10 | 49M27 | Secondary 41A25 | Computer Science, general | Strong regularity | Primary 47H10 | Real Functions | Affine-hull regularity | Generalized Douglas–Rachford algorithm | MATHEMATICS, APPLIED | FINITE CONVERGENCE | Generalized Douglas-Rachford algorithm | Quasi Fejer monotonicity | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EUCLIDEAN SPACES | NONCONVEX SETS | CONVEX | REGULARITY | ALTERNATING PROJECTIONS | Algorithms | Magnetic properties | Economic models | Convexity | Feasibility studies | Convergence

Quasi coercivity | 65K05 | Mathematics | 90C26 | Optimization | Quasi Fejér monotonicity | Cyclic algorithm | Linear convergence | Linear regularity | Superregularity | Operations Research/Decision Theory | 65K10 | 49M27 | Secondary 41A25 | Computer Science, general | Strong regularity | Primary 47H10 | Real Functions | Affine-hull regularity | Generalized Douglas–Rachford algorithm | MATHEMATICS, APPLIED | FINITE CONVERGENCE | Generalized Douglas-Rachford algorithm | Quasi Fejer monotonicity | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EUCLIDEAN SPACES | NONCONVEX SETS | CONVEX | REGULARITY | ALTERNATING PROJECTIONS | Algorithms | Magnetic properties | Economic models | Convexity | Feasibility studies | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 245 - 267

We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux...

Unstructured mesh | Finite volume method | Discrete maximum principle | Anisotropic diffusion equation | Positivity preserving property | Interpolation method | MAXIMUM PRINCIPLE | 2ND-ORDER | GRIDS | EQUATIONS | MONOTONICITY | LOCKING | PHYSICS, MATHEMATICAL | ELEMENT | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIPOINT FLUX APPROXIMATION | SCHEMES | Anisotropy | Methods | Green design

Unstructured mesh | Finite volume method | Discrete maximum principle | Anisotropic diffusion equation | Positivity preserving property | Interpolation method | MAXIMUM PRINCIPLE | 2ND-ORDER | GRIDS | EQUATIONS | MONOTONICITY | LOCKING | PHYSICS, MATHEMATICAL | ELEMENT | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIPOINT FLUX APPROXIMATION | SCHEMES | Anisotropy | Methods | Green design

Journal Article

Inverse Problems, ISSN 0266-5611, 12/2015, Volume 32, Issue 1, pp. 15011 - 15031

We consider a fractional diffusion equation (FDE) (C)D(t)(alpha)u = a(t)u(xx) with an undetermined time-dependent diffusion coefficient a(t). Firstly, for the...

reconstruct diffusion coefficient | monotonicity | fractional diffusion | fractional inverse problem | iteration algorithm | uniqueness | MATHEMATICS, APPLIED | DISPERSION | CALCULUS | PHYSICS, MATHEMATICAL | VISCOELASTICITY | ORDER | INVERSE PROBLEMS | Time dependence | Inverse problems | Mathematical analysis | Uniqueness | Diffusion | Diffusion coefficient | Coefficients | Regularity

reconstruct diffusion coefficient | monotonicity | fractional diffusion | fractional inverse problem | iteration algorithm | uniqueness | MATHEMATICS, APPLIED | DISPERSION | CALCULUS | PHYSICS, MATHEMATICAL | VISCOELASTICITY | ORDER | INVERSE PROBLEMS | Time dependence | Inverse problems | Mathematical analysis | Uniqueness | Diffusion | Diffusion coefficient | Coefficients | Regularity

Journal Article

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Full Text
Dirichlet Problem of a Delayed Reaction–Diffusion Equation on a Semi-infinite Interval

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2016, Volume 28, Issue 3, pp. 1007 - 1030

We consider a nonlocal delayed reaction–diffusion equation in a semi-infinite interval that describes mature population of a single species with two age stages...

34D23 | Mathematics | Dirichlet boundary condition | 35K57 | Delay | 34G25 | 39A30 | Reaction-diffusion equation | Ordinary Differential Equations | Nonlocal | Applications of Mathematics | Half line domain | Partial Differential Equations | MATHEMATICS, APPLIED | STABILITY | MONOTONICITY | NICHOLSONS BLOWFLIES EQUATION | MODEL | FUNCTIONAL-DIFFERENTIAL EQUATIONS | TRAVELING-WAVES | MATHEMATICS | CONVERGENCE | SYSTEMS | THRESHOLD DYNAMICS

34D23 | Mathematics | Dirichlet boundary condition | 35K57 | Delay | 34G25 | 39A30 | Reaction-diffusion equation | Ordinary Differential Equations | Nonlocal | Applications of Mathematics | Half line domain | Partial Differential Equations | MATHEMATICS, APPLIED | STABILITY | MONOTONICITY | NICHOLSONS BLOWFLIES EQUATION | MODEL | FUNCTIONAL-DIFFERENTIAL EQUATIONS | TRAVELING-WAVES | MATHEMATICS | CONVERGENCE | SYSTEMS | THRESHOLD DYNAMICS

Journal Article

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