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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
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
Journal Article
Optimization letters, ISSN 1862-4480, 2019, Volume 14, Issue 3, pp. 711 - 727
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
Journal Article
Taiwanese journal of mathematics, ISSN 1027-5487, 2014, Volume 18, Issue 2, pp. 419 - 433
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
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
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
Journal Article
Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2018, Volume 19, Issue 2, pp. 219 - 237
Journal Article
Numerical functional analysis and optimization, ISSN 1532-2467, 2019, Volume 40, Issue 6, pp. 621 - 653
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
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 7, pp. 2620 - 2642
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
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
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
Journal Article
Quarterly of Applied Mathematics, ISSN 0033-569X, 6/2002, Volume 60, Issue 2, pp. 301 - 316
Journal Article
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