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Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 1120 - 1129
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2014, Volume 161, Issue 2, pp. 478 - 489
Journal Article
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 07/2015, Volume 166, Issue 1, pp. 343 - 349
Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Br,zis and Lions... 
Convex minimization | MATHEMATICS, APPLIED | Monotone inclusion | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Proximal point algorithm | Rate of convergence | MONOTONE-OPERATORS | Algorithms | Studies | Mathematical analysis
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2016, Volume 62, pp. 55 - 62
The main purpose of this paper is to revisit the proximal point algorithms with over-relaxed -maximal -relaxed monotone mappings for solving variational... 
Over-relaxed [formula omitted]-maximal [formula omitted]-monotone mappings | Hilbert spaces | Proximal point algorithms | Variational inclusions | Over-relaxed A-maximal m-monotone mappings | VARIATIONAL-INEQUALITIES | MATHEMATICS, APPLIED | CONVERGENCE | MAPPINGS | MONOTONE-OPERATORS | Algorithms
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2015, Volume 166, Issue 1, pp. 343 - 349
Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Brézis and Lions... 
58E35 | Monotone inclusion | 65K15 | Mathematics | Theory of Computation | Proximal point algorithm | Optimization | Convex minimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Rate of convergence
Journal Article
SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2014, Volume 24, Issue 4, pp. 1614 - 1638
We propose a generalized proximal point algorithm (PPA) in the generic setting of finding a root of a maximal monotone operator. In addition to the classical... 
ALTERNATING DIRECTION METHOD | MATHEMATICS, APPLIED | PROGRAMS | LOCAL LINEAR CONVERGENCE | DECOMPOSITION | convex optimization | operator splitting methods | MULTIPLIERS | convergence rate | CONVEX MINIMIZATION | proximal point algorithm | MONOTONE-OPERATORS | Operators | Splitting | Algorithms | Roots | Benchmarking | Optimization | Convergence
Journal Article
Optimization Letters, ISSN 1862-4472, 4/2012, Volume 6, Issue 4, pp. 621 - 628
In this paper we construct a proximal point algorithm for maximal monotone operators with appropriate regularization parameters. We obtain the strong... 
Computational Intelligence | Operations Research/Decision Theory | Numerical and Computational Physics | Mathematics | Maximal monotone operator | Resolvent identity | Proximal point algorithm | Regularization | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPACES | OPERATORS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2019, Volume 343, pp. 67 - 89
This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric... 
Homogeneous domain of positivity | Compact Lie group | Proximal point algorithm | Hadamard manifold | Weighted Lpcenter of mass | Weighted L | center of mass | MATHEMATICS, APPLIED | Weighted L(P)center of mass | MATRICES | RIEMANNIAN-MANIFOLDS | GEOMETRY | Algorithms
Journal Article
Optimization Letters, ISSN 1862-4472, 05/2018, Volume 13, Issue 4, pp. 1 - 17
In this paper, we propose an asymmetric proximal point algorithm for solving variational inequality problems. The algorithm is asymmetric in the sense that the... 
Linear convergence | Asymmetric proximal term | Proximal point algorithm | Inexact APPA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 4, pp. 2235 - 2260
The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates (x(n)) given by x(n+1) = (I+lambda(n)... 
Proximal point algorithm | Stochastic approximation | Convex programming | MATHEMATICS, APPLIED | APPROXIMATION | STABILITY | convex programming | NETWORKS | SUM | proximal pointalgorithm | RESOURCE-ALLOCATION | CONVEX | SYSTEMS | stochastic approximation | HILBERT-SPACE | MONOTONE-OPERATORS | FUNCTIONALS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 2, pp. 544 - 555
Several strong convergence results involving two distinct four parameter proximal point algorithms are proved under different sets of assumptions on these... 
Regularization method | Weak convergence | Minimizer | Strong convergence | Monotone operator | Proximal point algorithm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | CONVERGENCE | MONOTONE-OPERATORS | FIXED-POINTS | Algorithms | Errors | Approximation | Equivalence | Norms | Nonlinearity | Regularization | Acceptability | Convergence
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 01/2020, Volume 147, pp. 1 - 18
The classical proximal point algorithm (PPA) requires a metric proximal parameter, which is positive definite and symmetric, because it plays the role of the... 
Linear convergence | Worst-case convergence rate | Variational inequality | Nonsymmetric proximal point algorithm | Big data | Algorithms
Journal Article
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 01/2019, Volume 96, Issue 1, pp. 199 - 215
Journal Article
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 09/2019, Volume 182, Issue 3, pp. 1019 - 1049
We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing... 
MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT DESCENT METHOD | MINIMIZATION | DECOMPOSITION | CONVERGENCE | Block coordinate minimization | Proximal point algorithm | LINEAR REGULARITY | Dykstra's splitting | LEAST-SQUARES | Algorithms
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 1019 - 1049
Journal Article
Journal of Global Optimization, ISSN 0925-5001, 12/2015, Volume 63, Issue 4, pp. 797 - 810
Journal Article
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 10/2019, Volume 42, Issue 8, pp. 1065 - 1078
In this work, we introduce a generalized contraction proximal point algorithm and use it to approximate common zeros of maximal monotone operators A and B in a... 
nonexpansive map | alternating method | contraction proximal point algorithm | resolvent operator | 47H09 | Maximal monotone operator | 47J25 | 47H05
Journal Article
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