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Mathematical programming, ISSN 1436-4646, 06/2016, Volume 162, Issue 1-2, pp. 83 - 112

We analyze the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG)...

68Q25 | 65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Stochastic gradient methods | 90C15 | First-order methods | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Convergence Rates | Combinatorics | 62L20 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Analysis | Algorithms | Studies | Convex analysis | Optimization | Mathematical analysis | Sag | Texts | Strategy | Mathematical models | Stochasticity | Sampling | Convergence

68Q25 | 65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Stochastic gradient methods | 90C15 | First-order methods | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Convergence Rates | Combinatorics | 62L20 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Analysis | Algorithms | Studies | Convex analysis | Optimization | Mathematical analysis | Sag | Texts | Strategy | Mathematical models | Stochasticity | Sampling | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 04/2015, Volume 156, Issue 1-2, pp. 433 - 484

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum...

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Big Data | Computer programming | Machine learning | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

68W20 | 68W40 | 65K05 | Theoretical, Mathematical and Computational Physics | 68W10 | 90C06 | Mathematics | Big data optimization | Parallel coordinate descent | Iteration complexity | 49M20 | Mathematical Methods in Physics | Partial separability | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Expected separable over-approximation | Huge-scale optimization | LASSO | 49M27 | Combinatorics | Composite objective | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Big data | Algorithms | Multiprocessing | Analysis | Methods | Studies | Optimization techniques | Big Data | Computer programming | Machine learning | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

Journal Article

Mathematical programming, ISSN 0025-5610, 12/2012, Volume 144, Issue 1-2, pp. 1 - 38

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function...

65K05 | Theoretical, Mathematical and Computational Physics | Block coordinate descent | 90C06 | Mathematics | Sparse regression | 90C05 | Iteration complexity | Gradient descent | Mathematical Methods in Physics | Gauss–Seidel method | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | Convex optimization | Coordinate relaxation | 90C25 | Numerical Analysis | Huge-scale optimization | LASSO | Combinatorics | Gauss-Seidel method | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Studies | Regression analysis | Optimization | Mathematical programming | Least squares method | Mathematical analysis | Blocking | Texts | Mathematical models | Iterative methods | Descent | Complexity

65K05 | Theoretical, Mathematical and Computational Physics | Block coordinate descent | 90C06 | Mathematics | Sparse regression | 90C05 | Iteration complexity | Gradient descent | Mathematical Methods in Physics | Gauss–Seidel method | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | Convex optimization | Coordinate relaxation | 90C25 | Numerical Analysis | Huge-scale optimization | LASSO | Combinatorics | Gauss-Seidel method | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Studies | Regression analysis | Optimization | Mathematical programming | Least squares method | Mathematical analysis | Blocking | Texts | Mathematical models | Iterative methods | Descent | Complexity

Journal Article

Mathematical programming, ISSN 1436-4646, 09/2009, Volume 128, Issue 1-2, pp. 321 - 353

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The...

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Matrix completion problem | Fixed point iterative method | Mathematical Methods in Physics | Nuclear norm minimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | Matrix rank minimization | Combinatorics | 93C41 | 68Q32 | Bregman distances | Singular value decomposition | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Algorithms | DNA microarrays | Management science | Analysis | Methods | Studies | Matrix | Iterative methods | Mathematical programming | Constraints | Images | Norms | Programming | Minimization | Matrices | Optimization

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Matrix completion problem | Fixed point iterative method | Mathematical Methods in Physics | Nuclear norm minimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical Analysis | Matrix rank minimization | Combinatorics | 93C41 | 68Q32 | Bregman distances | Singular value decomposition | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Algorithms | DNA microarrays | Management science | Analysis | Methods | Studies | Matrix | Iterative methods | Mathematical programming | Constraints | Images | Norms | Programming | Minimization | Matrices | Optimization

Journal Article

Mathematical programming, ISSN 1436-4646, 08/2007, Volume 117, Issue 1-2, pp. 387 - 423

We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained...

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 | 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 | Studies | Optimization | Mathematical programming

Journal Article

Mathematical programming, ISSN 1436-4646, 01/2018, Volume 175, Issue 1-2, pp. 69 - 107

The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function,...

Mathematical Methods in Physics | 65K05 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Management science | Linear systems | Formulations | Linear programming | Convexity | Convex analysis | Continuity (mathematics) | Optimization | Convergence

Mathematical Methods in Physics | 65K05 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Management science | Linear systems | Formulations | Linear programming | Convexity | Convex analysis | Continuity (mathematics) | Optimization | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 06/2013, Volume 146, Issue 1-2, pp. 37 - 75

We introduce the notion of inexact first-order oracle and analyze the behavior of several first-order methods of smooth convex optimization used with such an...

Gradient methods | Fast gradient methods | Theoretical, Mathematical and Computational Physics | 90C06 | Inexact oracle | Complexity bounds | Mathematics | First-order methods | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 90C60 | Smooth convex optimization | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Complexity theory | Analysis | Optimization | Mathematical programming | Functions (mathematics) | Permissible error | Accuracy | Smoothing | Mathematical analysis | Estimates | Regularization

Gradient methods | Fast gradient methods | Theoretical, Mathematical and Computational Physics | 90C06 | Inexact oracle | Complexity bounds | Mathematics | First-order methods | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 90C60 | Smooth convex optimization | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Complexity theory | Analysis | Optimization | Mathematical programming | Functions (mathematics) | Permissible error | Accuracy | Smoothing | Mathematical analysis | Estimates | Regularization

Journal Article

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Accelerated proximal stochastic dual coordinate ascent for regularized loss minimization

Mathematical programming, ISSN 1436-4646, 11/2014, Volume 155, Issue 1-2, pp. 105 - 145

We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure....

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | 90C15 | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Computer science | Jewish schools | Analysis | Machine learning | Studies | Stochastic models | Regression analysis | Optimization | Mathematical programming | Support vector machines | Ascent | Mathematical analysis | Regression | Stochasticity | Ridges | Logistics

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | 90C15 | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Computer science | Jewish schools | Analysis | Machine learning | Studies | Stochastic models | Regression analysis | Optimization | Mathematical programming | Support vector machines | Ascent | Mathematical analysis | Regression | Stochasticity | Ridges | Logistics

Journal Article

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From error bounds to the complexity of first-order descent methods for convex functions

Mathematical programming, ISSN 1436-4646, 11/2016, Volume 165, Issue 2, pp. 471 - 507

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a...

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Forward-backward method | Convex minimization | Mathematical Methods in Physics | Complexity of first-order methods | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | LASSO | Error bounds | KL inequality | Combinatorics | 90C60 | Compressed sensing | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Errors | Equivalence | Globalization | Inequalities | Constants | Shrinkage | Iterative methods | Regularization | Convex analysis | Descent | Methods | Complexity

65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | Forward-backward method | Convex minimization | Mathematical Methods in Physics | Complexity of first-order methods | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | LASSO | Error bounds | KL inequality | Combinatorics | 90C60 | Compressed sensing | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Errors | Equivalence | Globalization | Inequalities | Constants | Shrinkage | Iterative methods | Regularization | Convex analysis | Descent | Methods | Complexity

Journal Article

Mathematical programming, ISSN 1436-4646, 08/2014, Volume 152, Issue 1-2, pp. 615 - 642

In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in Nesterov (SIAM J Optim 22(2):341–362, 2012), Richtárik and Takáč...

Randomized block-coordinate descent | 65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | 90C05 | Iteration complexity | Mathematical Methods in Physics | Accelerated coordinate descent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | 90C25 | Numerical Analysis | Convergence rate | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Analysis | Methods | Machine learning | Studies | Mathematical models | Convex analysis | Mathematical programming | Convergence | Functions (mathematics) | Mathematical analysis | Blocking | Estimates | Descent | Optimization | Complexity

Randomized block-coordinate descent | 65K05 | Theoretical, Mathematical and Computational Physics | 90C06 | Mathematics | 90C05 | Iteration complexity | Mathematical Methods in Physics | Accelerated coordinate descent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | 90C25 | Numerical Analysis | Convergence rate | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Analysis | Methods | Machine learning | Studies | Mathematical models | Convex analysis | Mathematical programming | Convergence | Functions (mathematics) | Mathematical analysis | Blocking | Estimates | Descent | Optimization | Complexity

Journal Article

Mathematical programming, ISSN 1436-4646, 11/2015, Volume 159, Issue 1-2, pp. 371 - 401

We adapt the Douglas–Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization...

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | 90C90 | Mathematics | 90C26 | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Mathematical analysis | Optimization | Convergence | Mathematical programming | Splitting | Thresholds | Direct reduction | Clusters | Mathematical models

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C06 | 90C90 | Mathematics | 90C26 | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Mathematical analysis | Optimization | Convergence | Mathematical programming | Splitting | Thresholds | Direct reduction | Clusters | Mathematical models

Journal Article

Mathematical programming, ISSN 1436-4646, 12/2014, Volume 155, Issue 1-2, pp. 267 - 305

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable...

Nonconvex optimization | Theoretical, Mathematical and Computational Physics | Mini-batch of samples | 90C06 | Stochastic approximation | Mathematics | Zeroth-order method | First-order method | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | 49M37 | Combinatorics | Constrained stochastic programming | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Studies | Mathematical analysis | Approximations | Stochastic models | Optimization | Mathematical programming | Approximation | Programming | Mathematical models | Stochasticity | Complexity

Nonconvex optimization | Theoretical, Mathematical and Computational Physics | Mini-batch of samples | 90C06 | Stochastic approximation | Mathematics | Zeroth-order method | First-order method | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | 49M37 | Combinatorics | Constrained stochastic programming | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Studies | Mathematical analysis | Approximations | Stochastic models | Optimization | Mathematical programming | Approximation | Programming | Mathematical models | Stochasticity | Complexity

Journal Article