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

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

The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, 11/2013, Volume 69, Issue 5, pp. 1895 - 1906

.... In this paper, an MLE is derived to estimate the time of first change in the mean vector of a multivariate normal process...

Maximum likelihood estimator | Engineering | Statistical process control | Industrial and Production Engineering | Computer-Aided Engineering (CAD, CAE) and Design | Production/Logistics/Supply Chain | Change point | Multivariate normal process | Mechanical Engineering | Monotonic | INDIVIDUAL OBSERVATIONS | POISSON PROCESSES | SPC | CONTROL CHART | ENGINEERING, MANUFACTURING | AUTOMATION & CONTROL SYSTEMS | Energy costs | Maximum likelihood estimators | Acoustics | Multivariate analysis | Monte Carlo simulation | Control charts

Maximum likelihood estimator | Engineering | Statistical process control | Industrial and Production Engineering | Computer-Aided Engineering (CAD, CAE) and Design | Production/Logistics/Supply Chain | Change point | Multivariate normal process | Mechanical Engineering | Monotonic | INDIVIDUAL OBSERVATIONS | POISSON PROCESSES | SPC | CONTROL CHART | ENGINEERING, MANUFACTURING | AUTOMATION & CONTROL SYSTEMS | Energy costs | Maximum likelihood estimators | Acoustics | Multivariate analysis | Monte Carlo simulation | Control charts

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

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

Taiwanese journal of mathematics, ISSN 1027-5487, 2014, Volume 18, Issue 2, pp. 419 - 433

In this paper we consider the proximal point algorithm to approximate a singularity of a multivalued monotone vector field on a Hadamard manifold...

Mathematical manifolds | Riemann manifold | Mathematical monotonicity | Algorithms | Real numbers | Vector fields | Hilbert spaces | Mathematical functions | Mathematics | Perceptron convergence procedure | Maximal monotone operator | Resolvent | Proximal point algorithm | Hadamard manifold | Subdifferential | Convergence | MATHEMATICS | MONOTONE VECTOR-FIELDS | RESOLVENTS | OPERATORS

Mathematical manifolds | Riemann manifold | Mathematical monotonicity | Algorithms | Real numbers | Vector fields | Hilbert spaces | Mathematical functions | Mathematics | Perceptron convergence procedure | Maximal monotone operator | Resolvent | Proximal point algorithm | Hadamard manifold | Subdifferential | Convergence | MATHEMATICS | MONOTONE VECTOR-FIELDS | RESOLVENTS | OPERATORS

Journal Article

Operations research letters, ISSN 0167-6377, 2013, Volume 41, Issue 6, pp. 586 - 591

In this paper, an inexact proximal point algorithm concerned with the singularity of maximal monotone vector fields is introduced and studied on Hadamard manifolds, in which a relative error tolerance...

Inexact proximal point algorithm | Maximal monotone vector field | Hadamard manifold | VARIATIONAL-INEQUALITIES | EXTRAGRADIENT | PREINVEX FUNCTIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUASI-CONVEX | ITERATIVE ALGORITHMS | OPERATORS | RIEMANNIAN-MANIFOLDS | INVEX SETS | Algorithms | Manifolds | Operations research | Error analysis | Singularities | Tolerances | Fields (mathematics) | Optimization

Inexact proximal point algorithm | Maximal monotone vector field | Hadamard manifold | VARIATIONAL-INEQUALITIES | EXTRAGRADIENT | PREINVEX FUNCTIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUASI-CONVEX | ITERATIVE ALGORITHMS | OPERATORS | RIEMANNIAN-MANIFOLDS | INVEX SETS | Algorithms | Manifolds | Operations research | Error analysis | Singularities | Tolerances | Fields (mathematics) | Optimization

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 08/2015, Volume 41, Issue 4, pp. 1045 - 1059

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2019, Volume 21, Issue 1, pp. 1 - 23

In this paper, we consider the regularization method for exact as well as for inexact proximal point algorithms for finding the singularities of maximal monotone set-valued vector fields...

maximal monotone vector fields | Hadamard manifolds | proximal point algorithms | Mathematics | saddle point problems | Inclusion problems | regularization method | 47J22 | Mathematical Methods in Physics | 49J53 | Analysis | 49J40 | Mathematics, general | minimization problems | 47H05 | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | MATHEMATICS | SEMIGROUPS | PROJECTION | SETS | OPERATORS | STRONG-CONVERGENCE

maximal monotone vector fields | Hadamard manifolds | proximal point algorithms | Mathematics | saddle point problems | Inclusion problems | regularization method | 47J22 | Mathematical Methods in Physics | 49J53 | Analysis | 49J40 | Mathematics, general | minimization problems | 47H05 | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | MATHEMATICS | SEMIGROUPS | PROJECTION | SETS | OPERATORS | STRONG-CONVERGENCE

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2018, Volume 112, Issue 4, pp. 1521 - 1537

In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard manifolds, which is then utilized to state the finite...

KKM Maps | Equilibrium problem | Theoretical, Mathematical and Computational Physics | 49J40 | Maximal elements | Mathematics, general | Hadamard Manifold | Mathematics | Applications of Mathematics | 57p99 | EXISTENCE | TOPOLOGICAL-SPACES | THEOREM | VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | MATHEMATICS | MONOTONE | POINT | RIEMANNIAN-MANIFOLDS

KKM Maps | Equilibrium problem | Theoretical, Mathematical and Computational Physics | 49J40 | Maximal elements | Mathematics, general | Hadamard Manifold | Mathematics | Applications of Mathematics | 57p99 | EXISTENCE | TOPOLOGICAL-SPACES | THEOREM | VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | MATHEMATICS | MONOTONE | POINT | RIEMANNIAN-MANIFOLDS

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2018, Volume 19, Issue 2, pp. 219 - 237

This paper deals with the algorithm for computing the approximate solutions of variational inclusion problems in the setting of Hadamard manifolds. We discuss...

Maximal monotone vector fields | Monotone vector fields | Resolvent operators | Hadamard manifold | Variational inclusions | HILBERT-SPACES | MATHEMATICS, APPLIED | INEQUALITIES | maximal monotone vector fields | MONOTONE VECTOR-FIELDS | ACCRETIVE-OPERATORS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | MATHEMATICS | PROJECTION | monotone vector fields | RESOLVENTS | BANACH-SPACES | resolvent operators

Maximal monotone vector fields | Monotone vector fields | Resolvent operators | Hadamard manifold | Variational inclusions | HILBERT-SPACES | MATHEMATICS, APPLIED | INEQUALITIES | maximal monotone vector fields | MONOTONE VECTOR-FIELDS | ACCRETIVE-OPERATORS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | MATHEMATICS | PROJECTION | monotone vector fields | RESOLVENTS | BANACH-SPACES | resolvent operators

Journal Article

Numerical functional analysis and optimization, ISSN 1532-2467, 2019, Volume 40, Issue 6, pp. 621 - 653

In this article, we consider an inclusion problem which is defined by means of a sum of a single-valued vector field and a set-valued vector field defined on a Hadamard manifold...

Halpern-type algorithm | Mann-type algorithm | Riemannian metric | Hadamard manifolds | inclusions problems | maximal monotone vector fields | Fixed points | nonexpansive mappings | MATHEMATICS, APPLIED | INEQUALITIES | MONOTONE VECTOR-FIELDS | ITERATIVE ALGORITHMS | VALUED VARIATIONAL INCLUSIONS | PROJECTION | EQUILIBRIUM PROBLEMS | OPERATORS | Manifolds | Problems | Algorithms | Mapping | Fields (mathematics) | Optimization | Convergence

Halpern-type algorithm | Mann-type algorithm | Riemannian metric | Hadamard manifolds | inclusions problems | maximal monotone vector fields | Fixed points | nonexpansive mappings | MATHEMATICS, APPLIED | INEQUALITIES | MONOTONE VECTOR-FIELDS | ITERATIVE ALGORITHMS | VALUED VARIATIONAL INCLUSIONS | PROJECTION | EQUILIBRIUM PROBLEMS | OPERATORS | Manifolds | Problems | Algorithms | Mapping | Fields (mathematics) | Optimization | Convergence

Journal Article

Mathematics and Mechanics of Complex Systems, ISSN 2326-7186, 2013, Volume 1, Issue 2, pp. 149 - 176

Journal Article

Operations Research Letters, ISSN 0167-6377, 09/2014, Volume 42, Issue 6-7, pp. 383 - 387

In this paper, an estimate of convergence rate concerned with an inexact proximal point algorithm for the singularity of maximal monotone vector fields on Hadamard manifolds is discussed...

Convergence rate | Inexact proximal point algorithm | Maximal monotone vector field | Hadamard manifold | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BREGMAN DISTANCES | MONOTONE VECTOR-FIELDS | QUASI-CONVEX | EQUILIBRIUM PROBLEMS | CRITERION | Algorithms

Convergence rate | Inexact proximal point algorithm | Maximal monotone vector field | Hadamard manifold | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BREGMAN DISTANCES | MONOTONE VECTOR-FIELDS | QUASI-CONVEX | EQUILIBRIUM PROBLEMS | CRITERION | Algorithms

Journal Article

Theoretical and applied climatology, ISSN 0177-798X, 2018, Volume 136 (2019), Issue 3-4, pp. 1175 - 1184

.... Estimating an increasing trend in a distribution parameter is common in the field of isotonic regression...

Nonparametric estimation | Peaks-over-threshold | GPD | Isotonic regression | Central England temperature | Climatology | Earth Sciences | Atmospheric Sciences | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Atmospheric Protection/Air Quality Control/Air Pollution | Climate | Usage | Models | Algorithms | Analysis | Climatic analysis | Parameter estimation | Parameters | Statistical analysis | Computer simulation | Independent variables | Regression analysis | Maxima | Climatic extremes | Distribution | Mathematical models | Trends | Random variables | Maximum likelihood estimates | Iterative methods

Nonparametric estimation | Peaks-over-threshold | GPD | Isotonic regression | Central England temperature | Climatology | Earth Sciences | Atmospheric Sciences | Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution | Atmospheric Protection/Air Quality Control/Air Pollution | Climate | Usage | Models | Algorithms | Analysis | Climatic analysis | Parameter estimation | Parameters | Statistical analysis | Computer simulation | Independent variables | Regression analysis | Maxima | Climatic extremes | Distribution | Mathematical models | Trends | Random variables | Maximum likelihood estimates | Iterative methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 7, pp. 2620 - 2642

The maximum principle is one of the most important properties of solutions of partial differential equations. Its numerical analog, the discrete maximum...

Mesh refinement | M-matrix | Discrete maximum principle | Mimetic finite differences | Monotone scheme | Monotone matrix | CONVERGENCE ANALYSIS | VOLUME METHOD | APPROXIMATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATOR | STOKES PROBLEM | DIFFUSION-PROBLEMS | ERROR ESTIMATOR | Finite element method | Plasma physics | Anisotropy | Analysis | Methods | Parallelograms | Approximation | Discretization | Computation | Mathematical analysis | Maximum principle | Mathematical models

Mesh refinement | M-matrix | Discrete maximum principle | Mimetic finite differences | Monotone scheme | Monotone matrix | CONVERGENCE ANALYSIS | VOLUME METHOD | APPROXIMATIONS | PHYSICS, MATHEMATICAL | DISCRETIZATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATOR | STOKES PROBLEM | DIFFUSION-PROBLEMS | ERROR ESTIMATOR | Finite element method | Plasma physics | Anisotropy | Analysis | Methods | Parallelograms | Approximation | Discretization | Computation | Mathematical analysis | Maximum principle | Mathematical models

Journal Article

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, ISSN 1735-8515, 08/2015, Volume 41, Issue 4, pp. 1045 - 1059

...) - x is an element of M, sup(i >= 0) d(u(i), x) < +infinity, to a singularity of a multi-valued maximal monotone vector field A on a Hadamard manifold M, where {c(i)} and {theta...

MATHEMATICS | multivalued vector field | subdifferential | convergence | Hadamard manifold | minimization problem | EQUATIONS | MONOTONE VECTOR-FIELDS | Maximal monotone operator | PROXIMAL POINT ALGORITHM

MATHEMATICS | multivalued vector field | subdifferential | convergence | Hadamard manifold | minimization problem | EQUATIONS | MONOTONE VECTOR-FIELDS | Maximal monotone operator | PROXIMAL POINT ALGORITHM

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 2011, Volume 11, Issue 3, pp. 541 - 554

...(t) on a Hilbert space H, where the vector field f: H -> H is monotone, continuous and the forcing term e : R...

Hilbert spaces | Maximal monotone operators | Bohr-almost periodic | Besicovitch-almost periodic | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | maximal monotone operators

Hilbert spaces | Maximal monotone operators | Bohr-almost periodic | Besicovitch-almost periodic | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | maximal monotone operators

Journal Article

Optimization: International Symposium on Optimization and Optimal Control, February 2-6, 2009; Guest Editors: Valeri Obukhovskii and Jen-Chih Yao, ISSN 0233-1934, 06/2011, Volume 60, Issue 6, pp. 697 - 708

Given a maximal monotone vector field A on a Hadamard manifold, we devise a modified proximal point algorithm which, under reasonable assumptions, converges to a singular point...

maximal monotone | monotone vector field | modified proximal point algorithms | Hadamard manifold | Maximal monotone | Monotone vector field | Modified proximal point algorithms | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | ITERATIVE ALGORITHMS | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | CONVERGENCE | OPTIMIZATION | OPERATORS | RIEMANNIAN-MANIFOLDS | Manifolds | Operators | Algorithms | Mathematical analysis | Nonlinearity | Hilbert space | Vectors (mathematics) | Optimization

maximal monotone | monotone vector field | modified proximal point algorithms | Hadamard manifold | Maximal monotone | Monotone vector field | Modified proximal point algorithms | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | ITERATIVE ALGORITHMS | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | CONVERGENCE | OPTIMIZATION | OPERATORS | RIEMANNIAN-MANIFOLDS | Manifolds | Operators | Algorithms | Mathematical analysis | Nonlinearity | Hilbert space | Vectors (mathematics) | Optimization

Journal Article

20.
Full Text
GLOBAL SOLUTION TO A PHASE FIELD MODEL WITH IRREVERSIBLE AND CONSTRAINED PHASE EVOLUTION

Quarterly of Applied Mathematics, ISSN 0033-569X, 6/2002, Volume 60, Issue 2, pp. 301 - 316

This note deals with a nonlinear system of PDEs describing some irreversible phase change phenomena that account for a bounded limit velocity of the phase...

A priori knowledge | Phase velocity | Approximation | Logical proofs | Mathematical induction | Mathematical constants | Mathematical vectors | Mathematical models | Equations | Maximal monotone graphs | Phase field models | Doubly nonlinear evolution systems | Microscopic movements | microscopic movements | MATHEMATICS, APPLIED | doubly nonlinear evolution systems | maximal monotone graphs | phase field models

A priori knowledge | Phase velocity | Approximation | Logical proofs | Mathematical induction | Mathematical constants | Mathematical vectors | Mathematical models | Equations | Maximal monotone graphs | Phase field models | Doubly nonlinear evolution systems | Microscopic movements | microscopic movements | MATHEMATICS, APPLIED | doubly nonlinear evolution systems | maximal monotone graphs | phase field models

Journal Article

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