UofT Libraries is getting a new library services platform in January 2021.

Learn more about the change.

## Search Articles

Abstract and applied analysis, ISSN 1085-3375, 12/2004, Volume 2004, Issue 3, pp. 239 - 249

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 05/2014, Volume 23, Issue 2, pp. 205 - 221

Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve...

Geometry | 47H09 | Mathematics | 47H05 | 47H20 | Analysis | Physical Sciences | Mathematics, Applied | Science & Technology | School facilities | Algorithms | Methods | Education parks

Geometry | 47H09 | Mathematics | 47H05 | 47H20 | Analysis | Physical Sciences | Mathematics, Applied | Science & Technology | School facilities | Algorithms | Methods | Education parks

Journal Article

Computational optimization and applications, ISSN 1573-2894, 06/2016, Volume 66, Issue 1, pp. 75 - 96

In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and...

65K15 | 68W10 | Mathematics | Statistics, general | 65Y05 | Optimization | Generalized equilibrium problem | 47H10 | Equilibrium problem | Variational inequality | Convex and Discrete Geometry | Operations Research, Management Science | Operation Research/Decision Theory | Extragradient method | 47H05 | Gradient method | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Methods | Algorithms | Equality | Studies | Equilibrium | Operators | Computation | Inequalities | Projection | Mathematical models | Standards | Convergence

65K15 | 68W10 | Mathematics | Statistics, general | 65Y05 | Optimization | Generalized equilibrium problem | 47H10 | Equilibrium problem | Variational inequality | Convex and Discrete Geometry | Operations Research, Management Science | Operation Research/Decision Theory | Extragradient method | 47H05 | Gradient method | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Methods | Algorithms | Equality | Studies | Equilibrium | Operators | Computation | Inequalities | Projection | Mathematical models | Standards | Convergence

Journal Article

Advances in computational mathematics, ISSN 1572-9044, 11/2011, Volume 38, Issue 3, pp. 667 - 681

We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit...

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 08/2011, Volume 20, Issue 2, pp. 307 - 330

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued...

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | Physical Sciences | Mathematics, Applied | Science & Technology | Algorithms | Optimization and Control

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | Physical Sciences | Mathematics, Applied | Science & Technology | Algorithms | Optimization and Control

Journal Article

Numerical algorithms, ISSN 1572-9265, 09/2017, Volume 78, Issue 4, pp. 1045 - 1060

In this paper, we study the weak and strong convergence of two algorithms for solving Lipschitz continuous and monotone variational inequalities. The...

65K15 | Numeric Computing | 68W10 | Variational inequality problem | Theory of Computation | Monotone operator | 65Y05 | Tsengâ€™s extragradient method | Subgradient extragradient method | 47H10 | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | Extragradient method | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Equality | Convergence

65K15 | Numeric Computing | 68W10 | Variational inequality problem | Theory of Computation | Monotone operator | 65Y05 | Tsengâ€™s extragradient method | Subgradient extragradient method | 47H10 | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | Extragradient method | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Equality | Convergence

Journal Article

Mathematical programming, ISSN 0025-5610, 8/2018, Volume 170, Issue 2, pp. 417 - 444

We derive a new approximate version of the alternating direction method of multipliers (ADMM) which uses a relative error criterion. The new version is...

Monotone operators | Theoretical, Mathematical and Computational Physics | Mathematics | Convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Decomposition methods | 49M27 | Combinatorics | 47H05 | ADMM | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Management science | Algorithms | Splitting | Criteria

Monotone operators | Theoretical, Mathematical and Computational Physics | Mathematics | Convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Decomposition methods | 49M27 | Combinatorics | 47H05 | ADMM | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Management science | Algorithms | Splitting | Criteria

Journal Article

Journal of global optimization, ISSN 1573-2916, 08/2017, Volume 70, Issue 2, pp. 385 - 399

The paper considers two extragradient-like algorithms for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous...

65K15 | Pseudomonotone operator | Strongly pseudomonotone operator | 68W10 | Variational inequality problem | Mathematics | Monotone operator | Strongly monotone operator | 65Y05 | Optimization | Subgradient extragradient method | Projection method | 47H10 | Operations Research/Decision Theory | Extragradient method | Computer Science, general | 47H05 | Real Functions | Algorithms | Mathematical analysis | Hilbert space

65K15 | Pseudomonotone operator | Strongly pseudomonotone operator | 68W10 | Variational inequality problem | Mathematics | Monotone operator | Strongly monotone operator | 65Y05 | Optimization | Subgradient extragradient method | Projection method | 47H10 | Operations Research/Decision Theory | Extragradient method | Computer Science, general | 47H05 | Real Functions | Algorithms | Mathematical analysis | Hilbert space

Journal Article

Numerical algorithms, ISSN 1572-9265, 06/2015, Volume 71, Issue 3, pp. 519 - 540

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum...

Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence

Primal-dual algorithm | 65K05 | Subdifferential | Numeric Computing | Theory of Computation | Inertial splitting algorithm | Maximally monotone operator | Algorithms | Algebra | Resolvent | Convex optimization | 90C25 | Numerical Analysis | Computer Science | 47H05 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators | Splitting | Image processing | Inertial | Inclusions | Optimization | Convergence

Journal Article

Numerical algorithms, ISSN 1017-1398, 4/2019, Volume 80, Issue 4, pp. 1413 - 1436

The article introduces a new algorithm for solving a class of equilibrium problems involving strongly pseudomonotone bifunctions with a Lipschitz-type...

Proximal-like method | Numeric Computing | Theory of Computation | Regularized method | Strongly pseudomonotone bifunction | Algorithms | Algebra | 47J20 | Equilibrium problem | Numerical Analysis | Computer Science | Lipschitz-type bifunction | 47H05 | 47J25 | 65J15 | 91B50 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Convergence

Proximal-like method | Numeric Computing | Theory of Computation | Regularized method | Strongly pseudomonotone bifunction | Algorithms | Algebra | 47J20 | Equilibrium problem | Numerical Analysis | Computer Science | Lipschitz-type bifunction | 47H05 | 47J25 | 65J15 | 91B50 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 03/2018, Volume 174, Issue 1-2, pp. 453 - 471

The concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover, in particular, the optimality conditions...

Progressive hedging algorithm | Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Proximal point algorithm | Stochastic variational inequality problems | Mathematical Methods in Physics | 49J20 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Maximal monotone mappings | Stochastic programming problems | Stochastic complementarity problems | Combinatorics | 47H05 | Problem decomposition | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Hedging (Finance) | Algorithms | Multistage | Convexity | Nonlinear programming | Portfolio management

Progressive hedging algorithm | Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Proximal point algorithm | Stochastic variational inequality problems | Mathematical Methods in Physics | 49J20 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Maximal monotone mappings | Stochastic programming problems | Stochastic complementarity problems | Combinatorics | 47H05 | Problem decomposition | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Hedging (Finance) | Algorithms | Multistage | Convexity | Nonlinear programming | Portfolio management

Journal Article

12.
Full Text
Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

Mathematical programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 645 - 672

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The...

Monotone inclusion | Primal-dual algorithm | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Splitting algorithm | 49M27 | Block-iterative algorithm | Combinatorics | Asynchronous algorithm | 47H05 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Half spaces | Innovations | Decomposition | Inclusions | Linear operators | Convergence

Monotone inclusion | Primal-dual algorithm | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Splitting algorithm | 49M27 | Block-iterative algorithm | Combinatorics | Asynchronous algorithm | 47H05 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Half spaces | Innovations | Decomposition | Inclusions | Linear operators | Convergence

Journal Article

13.
Full Text
Convergence analysis of a new algorithm for strongly pseudomontone equilibrium problems

Numerical algorithms, ISSN 1572-9265, 05/2017, Volume 77, Issue 4, pp. 983 - 1001

The paper introduces and analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems involving strongly...

Proximal-like method | Numeric Computing | Theory of Computation | Strongly pseudomonotone bifunction | Algorithms | Algebra | 47J20 | Equilibrium problem | Numerical Analysis | Computer Science | Lipschitz-type bifunction | Extragradient method | 47H05 | 47J25 | 65J15 | 91B50 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Theorems | Iterative algorithms | Hilbert space | Iterative methods | Convergence

Proximal-like method | Numeric Computing | Theory of Computation | Strongly pseudomonotone bifunction | Algorithms | Algebra | 47J20 | Equilibrium problem | Numerical Analysis | Computer Science | Lipschitz-type bifunction | Extragradient method | 47H05 | 47J25 | 65J15 | 91B50 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Analysis | Theorems | Iterative algorithms | Hilbert space | Iterative methods | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 04/2018, Volume 177, Issue 1-2, pp. 225 - 253

In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglasâ€“Rachford splitting. When an...

65K15 | 65K05 | Theoretical, Mathematical and Computational Physics | Douglasâ€“Rachford splitting | Mathematics | Unbounded | Mathematical Methods in Physics | Conic programs | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Pathological | Infeasible | Combinatorics | 47H05 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Usage | Algorithms | Splitting | Subroutines | Optimization | Hyperplanes

65K15 | 65K05 | Theoretical, Mathematical and Computational Physics | Douglasâ€“Rachford splitting | Mathematics | Unbounded | Mathematical Methods in Physics | Conic programs | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Pathological | Infeasible | Combinatorics | 47H05 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Usage | Algorithms | Splitting | Subroutines | Optimization | Hyperplanes

Journal Article