Mathematical programming, ISSN 1436-4646, 04/2008, Volume 120, Issue 2, pp. 479 - 495

In this paper, we model any nonconvex quadratic program having a mix of binary and continuous variables as a linear program over the dual of the cone of...

90C20 | Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Mathematical and Computational Physics | Numerical Analysis | Mathematics | 90C26 | Combinatorics | Mathematics Subject Classification : 90C25 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Management science | Studies | Linear programming | Mathematical programming

90C20 | Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C25 | Mathematical and Computational Physics | Numerical Analysis | Mathematics | 90C26 | Combinatorics | Mathematics Subject Classification : 90C25 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Management science | Studies | Linear programming | Mathematical programming

Journal Article

Mathematical programming, ISSN 1436-4646, 07/2017, Volume 171, Issue 1-2, pp. 115 - 166

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein...

90C25 Convex programming | 90C47 Minimax problems | Mathematical Methods in Physics | 90C15 Stochastic programming | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Training | Economic models | Global optimization | Parameter uncertainty | Optimization techniques | Nonlinear programming | Monte Carlo simulation

90C25 Convex programming | 90C47 Minimax problems | Mathematical Methods in Physics | 90C15 Stochastic programming | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Training | Economic models | Global optimization | Parameter uncertainty | Optimization techniques | Nonlinear programming | Monte Carlo simulation

Journal Article

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, 12/2012, Volume 140, Issue 1, pp. 125 - 161

In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two terms: one is smooth and...

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 10/2014, Volume 155, Issue 1-2, pp. 57 - 79

The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are...

Alternating direction method of multipliers | Theoretical, Mathematical and Computational Physics | Mathematics | Convex programming | Convergence analysis | Mathematical Methods in Physics | Splitting methods | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 65K13 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Yuan (China) | Management techniques | Management science | Management | Analysis | Studies | Mathematical analysis | Convex analysis | Convergence | Mathematical programming | Functions (mathematics) | Multipliers | Divergence | Minimization | Optimization

Alternating direction method of multipliers | Theoretical, Mathematical and Computational Physics | Mathematics | Convex programming | Convergence analysis | Mathematical Methods in Physics | Splitting methods | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 65K13 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Yuan (China) | Management techniques | Management science | Management | Analysis | Studies | Mathematical analysis | Convex analysis | Convergence | Mathematical programming | Functions (mathematics) | Multipliers | Divergence | Minimization | Optimization

Journal Article

Numerische Mathematik, ISSN 0945-3245, 11/2014, Volume 130, Issue 3, pp. 567 - 577

This note proposes a novel approach to derive a worst-case
$$O(1/k)$$
O
(
1
/
k
)
convergence rate measured by the iteration complexity in a non-ergodic sense...

Mathematical Methods in Physics | 90C30 | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Yuan (China) | Methods

Mathematical Methods in Physics | 90C30 | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Yuan (China) | Methods

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

Applied mathematics & optimization, ISSN 1432-0606, 05/2017, Volume 78, Issue 3, pp. 613 - 641

For a finite/infinite family of closed convex sets with nonempty intersection in Hilbert space, we consider the (bounded) linear regularity property and the...

65J05 | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Projection algorithm | Mathematics | Mathematical Methods in Physics | Linear regularity | Convex feasibility problem | 41A25 | Calculus of Variations and Optimal Control; Optimization | 90C25 | 47H09 | Numerical and Computational Physics, Simulation | Physical Sciences | Mathematics, Applied | Science & Technology | Medical colleges | Algorithms | Analysis | Methods | Computational geometry | Projection | Feasibility | Hilbert space | Convexity | Regularity | Convergence

65J05 | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Projection algorithm | Mathematics | Mathematical Methods in Physics | Linear regularity | Convex feasibility problem | 41A25 | Calculus of Variations and Optimal Control; Optimization | 90C25 | 47H09 | Numerical and Computational Physics, Simulation | Physical Sciences | Mathematics, Applied | Science & Technology | Medical colleges | Algorithms | Analysis | Methods | Computational geometry | Projection | Feasibility | Hilbert space | Convexity | Regularity | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 11/2011, Volume 137, Issue 1-2, pp. 453 - 476

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of...

90C25 Convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C60 Abstract computational complexity for mathematical programming problems | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 68Q25 Analysis of algorithms & problem complexity | Mathematics | Combinatorics | Mathematics Subject Classification : 90C25 Convex programming | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Computer science | Electrical engineering | Mechanical properties | Algorithms | Hardness | Analysis | Studies | Polynomials | Multivariate analysis | Mathematical programming | Convexity | Complexity

90C25 Convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C60 Abstract computational complexity for mathematical programming problems | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 68Q25 Analysis of algorithms & problem complexity | Mathematics | Combinatorics | Mathematics Subject Classification : 90C25 Convex programming | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Computer science | Electrical engineering | Mechanical properties | Algorithms | Hardness | Analysis | Studies | Polynomials | Multivariate analysis | Mathematical programming | Convexity | Complexity

Journal Article

Mathematical programming, ISSN 0025-5610, 9/2011, Volume 129, Issue 1, pp. 69 - 89

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write...

68Q25 | Mathematical Methods in Physics | 65K05 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Mathematics Subject Classification : 90C25 | Analysis | Algorithms | Studies | Mathematical programming | Mathematical analysis | Exact solutions | Norms | Graphs | Minimization | Bypasses | Optimization

68Q25 | Mathematical Methods in Physics | 65K05 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Mathematics Subject Classification : 90C25 | Analysis | Algorithms | Studies | Mathematical programming | Mathematical analysis | Exact solutions | Norms | Graphs | Minimization | Bypasses | Optimization

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, 02/2015, Volume 156, Issue 1-2, pp. 59 - 99

In this paper, we generalize the well-known Nesterov’s accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex...

68Q25 | Nonconvex optimization | Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Stochastic programming | Complexity | Mathematical Methods in Physics | Accelerated gradient | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 62L20 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Convergence (Social sciences) | Studies | Computer programming | Stochastic models | Nonlinear programming | Policies | Approximation | Mathematical analysis | Programming | Stochasticity | Optimization | Convergence

68Q25 | Nonconvex optimization | Theoretical, Mathematical and Computational Physics | Mathematics | 90C15 | Stochastic programming | Complexity | Mathematical Methods in Physics | Accelerated gradient | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Combinatorics | 62L20 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Convergence (Social sciences) | Studies | Computer programming | Stochastic models | Nonlinear programming | Policies | Approximation | Mathematical analysis | Programming | Stochasticity | Optimization | 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 | Computer programming | 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 | Computer programming | Mathematical analysis | Blocking | Serials | Mathematical models | Iterative methods | Processors | Descent | Optimization

Journal Article