Journal of global optimization, ISSN 1573-2916, 2016, Volume 31, Issue 1, pp. 133 - 151

Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12--16...

monotone vector field | Hadamard manifold | Mathematics | Operation Research/Decision Theory | Computer Science, general | Optimization | global optimization | Real Functions | extragradient algorithm | Extragradient algorithm | Global optimization | Monotone vector field | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANIFOLDS | Analysis | Algorithms | Methamphetamine | Studies

monotone vector field | Hadamard manifold | Mathematics | Operation Research/Decision Theory | Computer Science, general | Optimization | global optimization | Real Functions | extragradient algorithm | Extragradient algorithm | Global optimization | Monotone vector field | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANIFOLDS | Analysis | Algorithms | Methamphetamine | Studies

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 06/2013, Volume 66, Issue 6, pp. 905 - 933

We show that any nondegenerate vector field u in \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document...

MATHEMATICS | VARIATIONAL RESOLUTIONS | MATHEMATICS, APPLIED | VALUED FUNCTIONS | MONOTONE | EVOLUTIONS

MATHEMATICS | VARIATIONAL RESOLUTIONS | MATHEMATICS, APPLIED | VALUED FUNCTIONS | MONOTONE | EVOLUTIONS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 5, pp. 1850 - 1861

Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced...

Riemannian manifolds | Monotone vector fields | Generalized invex functions | Invariant monotone vector fields | CRITERIA | MATHEMATICS | MATHEMATICS, APPLIED | CONVEXITY | ALGORITHM | GENERALIZED MONOTONICITY

Riemannian manifolds | Monotone vector fields | Generalized invex functions | Invariant monotone vector fields | CRITERIA | MATHEMATICS | MATHEMATICS, APPLIED | CONVEXITY | ALGORITHM | GENERALIZED MONOTONICITY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2016, Volume 271, Issue 6, pp. 1652 - 1690

We develop a “metrically selfdual” variational calculus for c-monotone vector fields between general manifolds X and Y, where c is a coupling on X×Y...

Optimal mass transport | Variational principles | Monotone maps on manifolds | POLAR FACTORIZATION | MATHEMATICS | VARIATIONAL RESOLUTIONS | NAVIER-STOKES | EQUATIONS | SYSTEMS | HAMILTONIANS | NONLINEAR EVOLUTIONS | VALUED FUNCTIONS | Local transit

Optimal mass transport | Variational principles | Monotone maps on manifolds | POLAR FACTORIZATION | MATHEMATICS | VARIATIONAL RESOLUTIONS | NAVIER-STOKES | EQUATIONS | SYSTEMS | HAMILTONIANS | NONLINEAR EVOLUTIONS | VALUED FUNCTIONS | Local transit

Journal Article

PACIFIC JOURNAL OF MATHEMATICS, ISSN 0030-8730, 06/2014, Volume 269, Issue 2, pp. 323 - 340

...)) of vector fields from Omega into R-d a Hamiltonian H on R-d x R-d x ... x R-d that is concave in the first variable, jointly convex in the last N-1 variables, and such that (u(1)(x), u(2)(x), ..., u(N-1)(x)) = del H-2,H-...,H-N(x, x, ..., x...

Krauss theorem | POLAR FACTORIZATION | MATHEMATICS | N-cyclically monotone vector fields | Mathematics - Optimization and Control

Krauss theorem | POLAR FACTORIZATION | MATHEMATICS | N-cyclically monotone vector fields | Mathematics - Optimization and Control

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2010, Volume 146, Issue 3, pp. 691 - 708

... J Optim Theory Appl (2010) 146: 691708 DOI 10.1007/s10957-010-9688-z Monotone and Accretive Vector Fields on Riemannian Manifolds J.H. Wang G. Lpez V. Martn...

Singularity | Monotone vector field | Hadamard manifold | Iterative algorithm | Convex function | Accretive vector field | Fixed point | EXISTENCE | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | UNIQUENESS | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | MAPPINGS | OPERATORS | Algorithms | Universities and colleges | Studies | Optimization | Manifolds | Approximation | Equivalence | Singularities | Mathematical analysis | Mapping | Vectors (mathematics)

Singularity | Monotone vector field | Hadamard manifold | Iterative algorithm | Convex function | Accretive vector field | Fixed point | EXISTENCE | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | PROXIMAL POINT ALGORITHM | UNIQUENESS | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | MAPPINGS | OPERATORS | Algorithms | Universities and colleges | Studies | Optimization | Manifolds | Approximation | Equivalence | Singularities | Mathematical analysis | Mapping | Vectors (mathematics)

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 2010, Volume 19, Issue 3, pp. 361 - 383

.... The resolvent of a set-valued vector field is defined in this setting and by means of this concept, a strong relationship between monotone vector fields and firmly nonexpansive mappings is established...

Geometry | Resolvent | Yosida approximation | Analysis | Hadamard manifold | Firmly nonexpansive mapping | Pseudo-contractive mapping | 49J40 | Mathematics | Maximal monotone vector field | 47H05 | EXISTENCE | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ACCRETIVE-OPERATORS | COACCRETIVE OPERATORS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | ASYMPTOTIC-BEHAVIOR | BANACH | VARIATIONAL-INEQUALITIES | ZEROS

Geometry | Resolvent | Yosida approximation | Analysis | Hadamard manifold | Firmly nonexpansive mapping | Pseudo-contractive mapping | 49J40 | Mathematics | Maximal monotone vector field | 47H05 | EXISTENCE | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ACCRETIVE-OPERATORS | COACCRETIVE OPERATORS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | ASYMPTOTIC-BEHAVIOR | BANACH | VARIATIONAL-INEQUALITIES | ZEROS

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 2002, Volume 101, Issue 2, pp. 185 - 232

.... Application of these Markov chain results leads to straightforward proofs of geometric ergodicity for a variety of SDEs, including problems with degenerate noise and for problems with locally Lipschitz vector fields...

Monotone | Additive noise | Stochastic differential equations | Langevin equation | Geometric ergodicity | Dissipative and gradient systems | Hypoelliptic and degenerate diffusions | Time-discretization | Geometric erdogicity | hypoelliptic and degenerate diffusions | LYAPUNOV EXPONENTS | STABILITY | STATISTICS & PROBABILITY | stochastic differential equations | geometric ergodicity | MARKOVIAN PROCESSES | monotone | dissipative and gradient systems | BOUNDS | additive noise | time-discretization | CONVERGENCE-RATES | Geometric ergodicity Stochastic differential equations Langevin equation Monotone Dissipative and gradient systems Additive noise Hypoelliptic and degenerate diffusions Time-discretization

Monotone | Additive noise | Stochastic differential equations | Langevin equation | Geometric ergodicity | Dissipative and gradient systems | Hypoelliptic and degenerate diffusions | Time-discretization | Geometric erdogicity | hypoelliptic and degenerate diffusions | LYAPUNOV EXPONENTS | STABILITY | STATISTICS & PROBABILITY | stochastic differential equations | geometric ergodicity | MARKOVIAN PROCESSES | monotone | dissipative and gradient systems | BOUNDS | additive noise | time-discretization | CONVERGENCE-RATES | Geometric ergodicity Stochastic differential equations Langevin equation Monotone Dissipative and gradient systems Additive noise Hypoelliptic and degenerate diffusions Time-discretization

Journal Article

JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2017, Volume 24, Issue 1, pp. 149 - 168

In this paper, a notion of pseudo-Jacobian of continuous vector fields on Riemannian manifolds is presented...

MATHEMATICS | Pseudo-Jacobian | NONSMOOTH ANALYSIS | Riemannian manifolds | SUBSETS | Lipschitz vector fields | Monotone vector fields

MATHEMATICS | Pseudo-Jacobian | NONSMOOTH ANALYSIS | Riemannian manifolds | SUBSETS | Lipschitz vector fields | Monotone vector fields

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 10/2008, Volume 4, Issue 1, pp. 107 - 135

Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials...

maximal monotone operator | Self-dual Lagrangian | Fenchel–Legendre duality | Mathematical Methods in Physics | Analysis | Mathematics, general | Mathematics | Primary 35F10, 35J65 | Secondary 47N10, 58E30 | Maximal monotone operator | Fenchel-Legendre duality | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTONIAN-SYSTEMS | RESOLUTIONS | EQUATIONS | ANTI-SELFDUAL LAGRANGIANS | OPERATORS

maximal monotone operator | Self-dual Lagrangian | Fenchel–Legendre duality | Mathematical Methods in Physics | Analysis | Mathematics, general | Mathematics | Primary 35F10, 35J65 | Secondary 47N10, 58E30 | Maximal monotone operator | Fenchel-Legendre duality | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTONIAN-SYSTEMS | RESOLUTIONS | EQUATIONS | ANTI-SELFDUAL LAGRANGIANS | OPERATORS

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 9/2019, Volume 50, Issue 3, pp. 625 - 644

.... Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow.

rho $$ ρ -monotone vector fields | 37L05 | Theoretical, Mathematical and Computational Physics | 37C10 | Nonlinear resolvent | Product formula | 47H09 | 30J99 | Mathematics, general | Mathematics | 30L99 | Evolution families | ρ-monotone vector fields | MATHEMATICS | rho-monotone vector fields

rho $$ ρ -monotone vector fields | 37L05 | Theoretical, Mathematical and Computational Physics | 37C10 | Nonlinear resolvent | Product formula | 47H09 | 30J99 | Mathematics, general | Mathematics | 30L99 | Evolution families | ρ-monotone vector fields | MATHEMATICS | rho-monotone vector fields

Journal Article

12.
Full Text
Proximal Point Algorithms on Hadamard Manifolds: Linear Convergence and Finite Termination

SIAM journal on optimization, ISSN 1095-7189, 2016, Volume 26, Issue 4, pp. 2696 - 2729

In the present paper, we consider inexact proximal point algorithms for finding singular points of multivalued vector fields on Hadamard manifolds...

Convergence rate | Hadamard manifolds | Inexact proximal point algorithms | Monotone vector fields | Finite termination | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | inexact proximal point algorithms | MONOTONE VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | finite termination | monotone vector fields | LOCALLY LIPSCHITZ FUNCTIONS | NEWTONS METHOD | COVARIANT ALPHA-THEORY | GENERALIZED EQUATIONS | METRIC SUBREGULARITY | BANACH-SPACES | convergence rate | RIEMANNIAN-MANIFOLDS

Convergence rate | Hadamard manifolds | Inexact proximal point algorithms | Monotone vector fields | Finite termination | MATHEMATICS, APPLIED | WEAK SHARP MINIMA | inexact proximal point algorithms | MONOTONE VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | finite termination | monotone vector fields | LOCALLY LIPSCHITZ FUNCTIONS | NEWTONS METHOD | COVARIANT ALPHA-THEORY | GENERALIZED EQUATIONS | METRIC SUBREGULARITY | BANACH-SPACES | convergence rate | RIEMANNIAN-MANIFOLDS

Journal Article

Mathematische Nachrichten, ISSN 1522-2616, 2019, Volume 292, Issue 10, pp. 2108 - 2128

We consider strongly monotone continuous planar vector fields with a finite number of fixed points...

47H10 | planar map | strongly monotone map | 47H05 | fixed point | winding number | MATHEMATICS | COMPETITION | DIFFERENTIAL-EQUATIONS | SYSTEMS

47H10 | planar map | strongly monotone map | 47H05 | fixed point | winding number | MATHEMATICS | COMPETITION | DIFFERENTIAL-EQUATIONS | SYSTEMS

Journal Article

Optimization letters, ISSN 1862-4480, 2019, Volume 14, Issue 3, pp. 711 - 727

In this paper, we consider the inclusion problems for maximal monotone set-valued vector fields defined on Hadamard manifolds...

Hadamard manifolds | Coercivity conditions | Existence results | Maximal monotone vector fields | Boundedness of solution set | Inclusion problems | MATHEMATICS, APPLIED | SET | CONVEXITY | PROXIMAL POINT ALGORITHMS | VARIATIONAL-INEQUALITIES | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | OPERATORS

Hadamard manifolds | Coercivity conditions | Existence results | Maximal monotone vector fields | Boundedness of solution set | Inclusion problems | MATHEMATICS, APPLIED | SET | CONVEXITY | PROXIMAL POINT ALGORITHMS | VARIATIONAL-INEQUALITIES | PROJECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | OPERATORS

Journal Article

SIAM journal on control and optimization, ISSN 1095-7138, 2012, Volume 50, Issue 4, pp. 2486 - 2514

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds...

Monotone vector fields | Proximal point algorithm | Riemannian manifold | Convexity of solution set | Variational inequalities | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | monotone vector fields | NEWTONS METHOD | MONOTONE | SPACES | HADAMARD MANIFOLDS | convexity of solution set | variational inequalities | proximal point algorithm | AUTOMATION & CONTROL SYSTEMS | Manifolds | Algorithms | Mathematical analysis | Inequalities | Convexity | Vectors (mathematics) | Optimization | Convergence

Monotone vector fields | Proximal point algorithm | Riemannian manifold | Convexity of solution set | Variational inequalities | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | monotone vector fields | NEWTONS METHOD | MONOTONE | SPACES | HADAMARD MANIFOLDS | convexity of solution set | variational inequalities | proximal point algorithm | AUTOMATION & CONTROL SYSTEMS | Manifolds | Algorithms | Mathematical analysis | Inequalities | Convexity | Vectors (mathematics) | Optimization | Convergence

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 5/2002, Volume 94, Issue 4, pp. 307 - 320

We introduce the concept of a strongly monotone vector field on a Riemannian manifold and give an example...

Mathematics, general | convex function | Mathematics | monotone vector field | Riemannian manifold | Monotone vector field | Convex function | MATHEMATICS | MANIFOLDS

Mathematics, general | convex function | Mathematics | monotone vector field | Riemannian manifold | Monotone vector field | Convex function | MATHEMATICS | MANIFOLDS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2014, Volume 34, Issue 4, pp. 1465 - 1480

Symmetric Monge-Kantorovich transport problems involving a cost function given by a family of vector fields were used by Ghoussoub-Moameni to establish polar decompositions of such vector fields...

Mass transport | M-cyclically monotone vector fields | M-cyclically antisymmetric functions | Monge-Kantorovich duality | POLAR FACTORIZATION | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTIONS | m-cyclically antisymmetric functions | VARIATIONAL RESOLUTIONS | m-cyclically monotone vector fields | VECTOR-FIELDS | OPTIMAL TRANSPORTATION

Mass transport | M-cyclically monotone vector fields | M-cyclically antisymmetric functions | Monge-Kantorovich duality | POLAR FACTORIZATION | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTIONS | m-cyclically antisymmetric functions | VARIATIONAL RESOLUTIONS | m-cyclically monotone vector fields | VECTOR-FIELDS | OPTIMAL TRANSPORTATION

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 473, Issue 2, pp. 866 - 891

We study equilibrium problem on general Riemannian manifolds, focusing on existence of solutions and the convexity properties of the solution set. Our approach...

Variational inequality problem | Equilibrium problem | Riemannian manifold | Proximal point algorithm | VARIATIONAL-INEQUALITIES | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | PRINCIPLE | NEWTON | Medical colleges | Algorithms | Numerical analysis | Game theory

Variational inequality problem | Equilibrium problem | Riemannian manifold | Proximal point algorithm | VARIATIONAL-INEQUALITIES | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | PRINCIPLE | NEWTON | Medical colleges | Algorithms | Numerical analysis | Game theory

Journal Article

Journal of global optimization, ISSN 1573-2916, 2014, Volume 61, Issue 3, pp. 553 - 573

Inexact proximal point methods are extended to find singular points for multivalued vector fields on Hadamard manifolds...

Operations Research/Decision Theory | Inexact proximal point algorithms | Hadamard manifolds | Mathematics | Monotone vector fields | Primary 49J40 | Secondary 58D17 | Computer Science, general | Optimization | Real Functions | Convergence analysis | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | UNIQUENESS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | BANACH-SPACES | OPERATORS | RIEMANNIAN-MANIFOLDS | Analysis | Algorithms | Studies | Optimization algorithms | Linear algebra | Manifolds | Inequalities | Texts | Lithium | Fields (mathematics) | Convergence

Operations Research/Decision Theory | Inexact proximal point algorithms | Hadamard manifolds | Mathematics | Monotone vector fields | Primary 49J40 | Secondary 58D17 | Computer Science, general | Optimization | Real Functions | Convergence analysis | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | UNIQUENESS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | BANACH-SPACES | OPERATORS | RIEMANNIAN-MANIFOLDS | Analysis | Algorithms | Studies | Optimization algorithms | Linear algebra | Manifolds | Inequalities | Texts | Lithium | Fields (mathematics) | Convergence

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2019, Volume 276, Issue 4, pp. 1201 - 1243

.... In this paper, we show how self-dual variational calculus leads to variational solutions of various stochastic partial differential equations driven by monotone vector fields...

Maximal monotone vector fields | Bolza duality | Stochastic PDE | Self-dual variational calculus | MATHEMATICS | PARABOLIC EQUATIONS | RESOLUTIONS | NAVIER-STOKES | LAGRANGIANS | PRINCIPLE | HAMILTONIANS | OPERATORS

Maximal monotone vector fields | Bolza duality | Stochastic PDE | Self-dual variational calculus | MATHEMATICS | PARABOLIC EQUATIONS | RESOLUTIONS | NAVIER-STOKES | LAGRANGIANS | PRINCIPLE | HAMILTONIANS | OPERATORS

Journal Article

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