TOP, ISSN 1134-5764, 04/2018, Volume 26, Issue 1, pp. 110 - 145

This paper describes an algorithm for solving structured nonsmooth convex optimization problems using the optimal subgradient algorithm (OSGA...

First-order black-box information | Structured nonsmooth convex optimization | Subgradient methods | Optimal complexity | Proximity operator | EQUATIONS | ALGORITHMS | NEWTON METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | GUIDED CONJUGATE GRADIENTS | DOUBLE SMOOTHING TECHNIQUE | REGULARIZATION

First-order black-box information | Structured nonsmooth convex optimization | Subgradient methods | Optimal complexity | Proximity operator | EQUATIONS | ALGORITHMS | NEWTON METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | GUIDED CONJUGATE GRADIENTS | DOUBLE SMOOTHING TECHNIQUE | REGULARIZATION

Journal Article

SIAM journal on optimization, ISSN 1095-7189, 2016, Volume 26, Issue 2, pp. 891 - 921

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly nondifferentiable,...

Nonsmooth optimization | Nonconvex optimization | Generalized projection | Proximal algorithms | PROJECTED GRADIENT METHODS | MATHEMATICS, APPLIED | proximal algorithms | MINIMIZATION | CONVEX | EUCLIDEAN DISTANCES | PROXIMAL POINT ALGORITHMS | SUBGRADIENT METHODS | CONVERGENCE | nonconvex optimization | nonsmooth optimization | generalized projection

Nonsmooth optimization | Nonconvex optimization | Generalized projection | Proximal algorithms | PROJECTED GRADIENT METHODS | MATHEMATICS, APPLIED | proximal algorithms | MINIMIZATION | CONVEX | EUCLIDEAN DISTANCES | PROXIMAL POINT ALGORITHMS | SUBGRADIENT METHODS | CONVERGENCE | nonconvex optimization | nonsmooth optimization | generalized projection

Journal Article

Mathematical programming, ISSN 1436-4646, 2007, Volume 117, Issue 1-2, pp. 387 - 423

.... This problem includes as special cases bound-constrained optimization and smooth optimization with ℓ1-regularization. We propose a (block...

Global convergence | 65K05 | Mathematical and Computational Physics | 90C06 | Error bound | Mathematics | 90C26 | Coordinate descent | Linear convergence rate | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | 90C55 | Nonsmooth optimization | 49M27 | 49M37 | Combinatorics | REGRESSION | MATHEMATICS, APPLIED | error bound | linear convergence rate | ASCENT METHODS | global convergence | ALGORITHM | coordinate descent | SUM | CONVEX FUNCTION | nonsmooth optimization | LINEAR CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ROBUST | Studies | Optimization | Mathematical programming

Global convergence | 65K05 | Mathematical and Computational Physics | 90C06 | Error bound | Mathematics | 90C26 | Coordinate descent | Linear convergence rate | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | 90C55 | Nonsmooth optimization | 49M27 | 49M37 | Combinatorics | REGRESSION | MATHEMATICS, APPLIED | error bound | linear convergence rate | ASCENT METHODS | global convergence | ALGORITHM | coordinate descent | SUM | CONVEX FUNCTION | nonsmooth optimization | LINEAR CONVERGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ROBUST | Studies | Optimization | Mathematical programming

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 2/2015, Volume 61, Issue 2, pp. 325 - 340

In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network...

Gaussian smoothing | Convex optimization | Operations Research/Decision Theory | Distributed algorithm | Mathematics | Computer Science, general | Gradient-free method | Optimization | Real Functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBGRADIENT METHODS | CONSENSUS | Algorithms | School construction | Studies | Optimization algorithms | Mathematical analysis | Networks | Computer simulation | Smoothing | Texts | Mathematical models | Gaussian | Convergence

Gaussian smoothing | Convex optimization | Operations Research/Decision Theory | Distributed algorithm | Mathematics | Computer Science, general | Gradient-free method | Optimization | Real Functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBGRADIENT METHODS | CONSENSUS | Algorithms | School construction | Studies | Optimization algorithms | Mathematical analysis | Networks | Computer simulation | Smoothing | Texts | Mathematical models | Gaussian | Convergence

Journal Article

1992, ISBN 9789810207731, xii, 254

Book

International journal of robust and nonlinear control, ISSN 1099-1239, 2019, Volume 29, Issue 10, pp. 3252 - 3266

Summary This paper investigates a general monotropic optimization problem for continuous...

continuous‐time networks | general monotropic optimization problems | distributed convex optimization | nonsmooth analysis | Analysis | Algorithms | Nonlinear programming | Computer simulation | Optimization

continuous‐time networks | general monotropic optimization problems | distributed convex optimization | nonsmooth analysis | Analysis | Algorithms | Nonlinear programming | Computer simulation | Optimization

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2018, Volume 56, Issue 6, pp. 3973 - 3993

This paper studies distributed algorithms for the nonsmooth extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure...

Extended monotropic optimization | Differential inclusions | Nonsmooth convex functions | Distributed algorithms | Decomposition methods | ECONOMIC-DISPATCH | MATHEMATICS, APPLIED | NETWORK | CONVEX-OPTIMIZATION | OPTIMAL CONSENSUS | GENETIC ALGORITHM | decomposition methods | PROJECTION | distributed algorithms | extended monotropic optimization | nonsmooth convex functions | differential inclusions | GRADIENT ALGORITHM | AUTOMATION & CONTROL SYSTEMS

Extended monotropic optimization | Differential inclusions | Nonsmooth convex functions | Distributed algorithms | Decomposition methods | ECONOMIC-DISPATCH | MATHEMATICS, APPLIED | NETWORK | CONVEX-OPTIMIZATION | OPTIMAL CONSENSUS | GENETIC ALGORITHM | decomposition methods | PROJECTION | distributed algorithms | extended monotropic optimization | nonsmooth convex functions | differential inclusions | GRADIENT ALGORITHM | AUTOMATION & CONTROL SYSTEMS

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2018, Volume 72, Issue 1, pp. 115 - 157

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability...

Alternating direction method of multipliers | 90C06 | Mathematics | Structured nonconvex optimization | 90C26 | Statistics, general | Optimization | Iteration complexity | epsilon $$ ϵ -Stationary | Conditional gradient method | Operations Research/Decision Theory | Convex and Discrete Geometry | Block coordinate descent method | Operations Research, Management Science | 90C60 | ϵ-Stationary | SPARSITY | MATHEMATICS, APPLIED | MULTIPLIERS | MULTISTAGE CONVEX RELAXATION | VARIABLE SELECTION | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | E-Stationary | MINIMIZATION | CONVERGENCE | SUBGRADIENT | Analysis | Management science | Algorithms | Robustness (mathematics) | Constraint modelling | Nonlinear programming | Iterative methods | Convergence | Complexity

Alternating direction method of multipliers | 90C06 | Mathematics | Structured nonconvex optimization | 90C26 | Statistics, general | Optimization | Iteration complexity | epsilon $$ ϵ -Stationary | Conditional gradient method | Operations Research/Decision Theory | Convex and Discrete Geometry | Block coordinate descent method | Operations Research, Management Science | 90C60 | ϵ-Stationary | SPARSITY | MATHEMATICS, APPLIED | MULTIPLIERS | MULTISTAGE CONVEX RELAXATION | VARIABLE SELECTION | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | E-Stationary | MINIMIZATION | CONVERGENCE | SUBGRADIENT | Analysis | Management science | Algorithms | Robustness (mathematics) | Constraint modelling | Nonlinear programming | Iterative methods | Convergence | Complexity

Journal Article

Journal of nonlinear science, ISSN 1432-1467, 2018, Volume 29, Issue 4, pp. 1247 - 1272

This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure...

34D23 | Nonsmooth convex optimization | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | 68W15 | Distributed multi-agent coordination | 90C35 | 90C25 | 49J52 | Analysis | Mathematical and Computational Engineering | Continuous-time optimization algorithms | Saddle-point dynamics | 34A60 | MATHEMATICS, APPLIED | NETWORK | DESIGN | STABILITY | DECOMPOSITION | CONSENSUS | PHYSICS, MATHEMATICAL | MECHANICS | NASH EQUILIBRIA | CONVERGENCE | SYSTEMS | Algorithms | Mechanical engineering | Mathematical optimization | Aerospace engineering

34D23 | Nonsmooth convex optimization | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | 68W15 | Distributed multi-agent coordination | 90C35 | 90C25 | 49J52 | Analysis | Mathematical and Computational Engineering | Continuous-time optimization algorithms | Saddle-point dynamics | 34A60 | MATHEMATICS, APPLIED | NETWORK | DESIGN | STABILITY | DECOMPOSITION | CONSENSUS | PHYSICS, MATHEMATICAL | MECHANICS | NASH EQUILIBRIA | CONVERGENCE | SYSTEMS | Algorithms | Mechanical engineering | Mathematical optimization | Aerospace engineering

Journal Article

Mathematical programming, ISSN 1436-4646, 2015, Volume 156, Issue 1-2, pp. 125 - 159

We propose a bundle method for minimizing nonsmooth convex functions that combines both the level and the proximal stabilizations...

Proximal bundle method | 65K05 | Theoretical, Mathematical and Computational Physics | Inexact oracle | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Level bundle method | 90C25 | Numerical Analysis | Nonsmooth optimization | Combinatorics | NONDIFFERENTIABLE OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | APPROXIMATIONS | ORACLES | Analysis | Methods | Algorithms | Studies | Computer programming | Convex analysis | Bundling | Computational geometry | Stabilization | Lagrange multipliers | Mathematical analysis | Mathematical models | Optimization

Proximal bundle method | 65K05 | Theoretical, Mathematical and Computational Physics | Inexact oracle | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Level bundle method | 90C25 | Numerical Analysis | Nonsmooth optimization | Combinatorics | NONDIFFERENTIABLE OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | APPROXIMATIONS | ORACLES | Analysis | Methods | Algorithms | Studies | Computer programming | Convex analysis | Bundling | Computational geometry | Stabilization | Lagrange multipliers | Mathematical analysis | Mathematical models | Optimization

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2014, Volume 166, Issue 3, pp. 889 - 905

We propose an efficient diagonal bundle method for sparse nonsmooth, possibly nonconvex optimization...

Diagonal variable metric methods | 65K05 | Bundle methods | Sparse problems | Mathematics | Theory of Computation | Optimization | Nondifferentiable optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | NONCONVEX OPTIMIZATION | VARIABLE-METRIC METHOD | MATHEMATICS, APPLIED | ALGORITHM | CLASSIFICATION | QUASI-NEWTON MATRICES | CONVEX-OPTIMIZATION | PROXIMITY CONTROL | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | FORMULATIONS | Studies | Optimization techniques | Mathematical analysis | Bundling | Mathematical models | Convergence | Extreme values

Diagonal variable metric methods | 65K05 | Bundle methods | Sparse problems | Mathematics | Theory of Computation | Optimization | Nondifferentiable optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | NONCONVEX OPTIMIZATION | VARIABLE-METRIC METHOD | MATHEMATICS, APPLIED | ALGORITHM | CLASSIFICATION | QUASI-NEWTON MATRICES | CONVEX-OPTIMIZATION | PROXIMITY CONTROL | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | FORMULATIONS | Studies | Optimization techniques | Mathematical analysis | Bundling | Mathematical models | Convergence | Extreme values

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2018, Volume 72, Issue 1, pp. 1 - 43

We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems...

Quadratic penalty method | Proximal alternating algorithm | 90-08 | Mathematics | Statistics, general | First-order methods | Optimization | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Convergence rate | Constrained convex optimization | Operations Research, Management Science | Accelerated scheme | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE RATE ANALYSIS | DECOMPOSITION | GRADIENT | Management science | Algorithms | Computational geometry | Adaptive algorithms | Convexity | Iterative methods | Convex analysis | Convergence

Quadratic penalty method | Proximal alternating algorithm | 90-08 | Mathematics | Statistics, general | First-order methods | Optimization | 90C25 | Operations Research/Decision Theory | Convex and Discrete Geometry | Convergence rate | Constrained convex optimization | Operations Research, Management Science | Accelerated scheme | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE RATE ANALYSIS | DECOMPOSITION | GRADIENT | Management science | Algorithms | Computational geometry | Adaptive algorithms | Convexity | Iterative methods | Convex analysis | Convergence

Journal Article

PLoS ONE, ISSN 1932-6203, 01/2018, Volume 13, Issue 1, p. e0189290

.... Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective function smooth...

CONVERGENCE ANALYSIS | CONVEX NONDIFFERENTIABLE MINIMIZATION | GRADIENT METHODS | PROGRAMS | MEMORY BUNDLE METHOD | MULTIDISCIPLINARY SCIENCES | EQUATIONS | VERSION | QUASI-NEWTON METHODS | TRUST REGION ALGORITHM | UNCONSTRAINED OPTIMIZATION | Usage | Algorithms | Mathematical optimization | Analysis | Computer memory | Problems | Applied mathematics | Constraint modelling | Mathematical models | Linear equations | Objective function | Regularization | Convex analysis | Optimization | Mathematical programming

CONVERGENCE ANALYSIS | CONVEX NONDIFFERENTIABLE MINIMIZATION | GRADIENT METHODS | PROGRAMS | MEMORY BUNDLE METHOD | MULTIDISCIPLINARY SCIENCES | EQUATIONS | VERSION | QUASI-NEWTON METHODS | TRUST REGION ALGORITHM | UNCONSTRAINED OPTIMIZATION | Usage | Algorithms | Mathematical optimization | Analysis | Computer memory | Problems | Applied mathematics | Constraint modelling | Mathematical models | Linear equations | Objective function | Regularization | Convex analysis | Optimization | Mathematical programming

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 3/2009, Volume 140, Issue 3, pp. 513 - 535

...J Optim Theory Appl (2009) 140: 513–535 DOI 10.1007/s10957-008-9458-3 Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable...

ℓ 1 -regularization | Global convergence | Mathematics | Theory of Computation | Optimization | Support vector machines | Linear convergence rate | Bilevel optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Linear constraints | Complexity bound | Nonsmooth optimization | Engineering, general | Applications of Mathematics | Coordinate gradient descent | regularization | MATHEMATICS, APPLIED | l-regularization | DECOMPOSITION | SUM | CONVEX FUNCTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ROBUST | TIME ALGORITHMS | CONVERGENCE | Mathematical optimization | Methods | Studies | Mathematical programming

ℓ 1 -regularization | Global convergence | Mathematics | Theory of Computation | Optimization | Support vector machines | Linear convergence rate | Bilevel optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Linear constraints | Complexity bound | Nonsmooth optimization | Engineering, general | Applications of Mathematics | Coordinate gradient descent | regularization | MATHEMATICS, APPLIED | l-regularization | DECOMPOSITION | SUM | CONVEX FUNCTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ROBUST | TIME ALGORITHMS | CONVERGENCE | Mathematical optimization | Methods | Studies | Mathematical programming

Journal Article

16.
Full Text
A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

SIAM journal on optimization, ISSN 1095-7189, 2018, Volume 28, Issue 1, pp. 96 - 134

We propose a new and low per-iteration complexity first-order primal-dual optimization framework for a convex optimization template with broad applications...

Separable convex minimization | Homotopy | Augmented Lagrangian | First-order primal-dual methods | Gap reduction technique | Smoothing techniques | Parallel and distributed computation | MATHEMATICS, APPLIED | smoothing techniques | ALGORITHM | CONVERGENCE RATE ANALYSIS | DECOMPOSITION | homotopy | first-order primal-dual methods | VARIATIONAL-INEQUALITIES | EXTRAGRADIENT | ALTERNATING DIRECTION METHOD | separable convex minimization | ITERATION-COMPLEXITY | parallel and distributed computation | gap reduction technique | augmented Lagrangian | SADDLE-POINT | GEOMETRY

Separable convex minimization | Homotopy | Augmented Lagrangian | First-order primal-dual methods | Gap reduction technique | Smoothing techniques | Parallel and distributed computation | MATHEMATICS, APPLIED | smoothing techniques | ALGORITHM | CONVERGENCE RATE ANALYSIS | DECOMPOSITION | homotopy | first-order primal-dual methods | VARIATIONAL-INEQUALITIES | EXTRAGRADIENT | ALTERNATING DIRECTION METHOD | separable convex minimization | ITERATION-COMPLEXITY | parallel and distributed computation | gap reduction technique | augmented Lagrangian | SADDLE-POINT | GEOMETRY

Journal Article