Mathematical Programming, ISSN 0025-5610, 8/2014, Volume 146, Issue 1, pp. 459 - 494

We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems....

Gauss-Seidel method | Kurdyka–Łojasiewicz property | Theoretical, Mathematical and Computational Physics | Block coordinate descent | Alternating minimization | Mathematics | 90C26 | Nonconvex-nonsmooth minimization | Proximal forward-backward | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 65K10 | 49M27 | 49M37 | Combinatorics | 47J25 | Sparse nonnegative matrix factorization | Kurdyka-Łojasiewicz property | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | Kurdyka-Lojasiewicz property | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | NONNEGATIVE MATRIX FACTORIZATION | Analysis | Management science | Algorithms | Studies | Data smoothing | Mathematical programming | Functions (mathematics) | Construction | Mathematical analysis | Palm | Byproducts | Minimization | Optimization | Optimization and Control

Gauss-Seidel method | Kurdyka–Łojasiewicz property | Theoretical, Mathematical and Computational Physics | Block coordinate descent | Alternating minimization | Mathematics | 90C26 | Nonconvex-nonsmooth minimization | Proximal forward-backward | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 65K10 | 49M27 | 49M37 | Combinatorics | 47J25 | Sparse nonnegative matrix factorization | Kurdyka-Łojasiewicz property | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | Kurdyka-Lojasiewicz property | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | NONNEGATIVE MATRIX FACTORIZATION | Analysis | Management science | Algorithms | Studies | Data smoothing | Mathematical programming | Functions (mathematics) | Construction | Mathematical analysis | Palm | Byproducts | Minimization | Optimization | Optimization and Control

Journal Article

Mathematical Programming, ISSN 0025-5610, 12/2012, Volume 136, Issue 1, pp. 155 - 182

We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to...

Mathematical Methods in Physics | 90C20 Quadratic programming | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C57 Polyhedral combinatorics | Theoretical, Mathematical and Computational Physics | Numerical Analysis | 90C26 Global optimization | branch & bound | Mathematics | Combinatorics | 90C57 Polyhedral combinatorics; branch & bound | Mathematics Subject Classification: 90C26 Global optimization | BRANCH | MATHEMATICS, APPLIED | NETWORKS | NONCONVEX NLPS | BILINEAR PROGRAMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALPHA-BB | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DISTILLATION SEQUENCES | CONVEX | BOUND ALGORITHM | POOLING PROBLEMS | CUT ALGORITHM | Studies | Quadratic programming | Optimization | Trees | Computation | Multivariable | Agglomeration | Standards | Mathematical programming

Mathematical Methods in Physics | 90C20 Quadratic programming | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 90C57 Polyhedral combinatorics | Theoretical, Mathematical and Computational Physics | Numerical Analysis | 90C26 Global optimization | branch & bound | Mathematics | Combinatorics | 90C57 Polyhedral combinatorics; branch & bound | Mathematics Subject Classification: 90C26 Global optimization | BRANCH | MATHEMATICS, APPLIED | NETWORKS | NONCONVEX NLPS | BILINEAR PROGRAMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALPHA-BB | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DISTILLATION SEQUENCES | CONVEX | BOUND ALGORITHM | POOLING PROBLEMS | CUT ALGORITHM | Studies | Quadratic programming | Optimization | Trees | Computation | Multivariable | Agglomeration | Standards | Mathematical programming

Journal Article

Mathematical Programming, ISSN 0025-5610, 12/2013, Volume 142, Issue 1, pp. 397 - 434

Minimization with orthogonality constraints (e.g., $$X^\top X = I$$ ) and/or spherical constraints (e.g., $$\Vert x\Vert _2 = 1$$ ) has wide applications in...

Nearest correlation matrix | Invariant subspace | 65K05 | Theoretical, Mathematical and Computational Physics | Curvilinear search | Maxcut SDP | Mathematics | 90C26 | Eigenvalue and eigenvector | Quadratic assignment problem | 90C27 | Orthogonality constraint | Mathematical Methods in Physics | Cayley transformation | 90C30 | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Stiefel manifold | Numerical Analysis | 90C22 | Spherical constraint | 49Q99 | Combinatorics | MATHEMATICS, APPLIED | ALGORITHM | DECOMPOSITION | FORMULATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | BARZILAI | MATRICES | RANK REDUCTION | FLOWS | SEMIDEFINITE PROGRAMS | Methods | Algorithms | Studies | Polynomials | Topological manifolds | Analysis | Optimization | Mathematical programming

Nearest correlation matrix | Invariant subspace | 65K05 | Theoretical, Mathematical and Computational Physics | Curvilinear search | Maxcut SDP | Mathematics | 90C26 | Eigenvalue and eigenvector | Quadratic assignment problem | 90C27 | Orthogonality constraint | Mathematical Methods in Physics | Cayley transformation | 90C30 | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Stiefel manifold | Numerical Analysis | 90C22 | Spherical constraint | 49Q99 | Combinatorics | MATHEMATICS, APPLIED | ALGORITHM | DECOMPOSITION | FORMULATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | BARZILAI | MATRICES | RANK REDUCTION | FLOWS | SEMIDEFINITE PROGRAMS | Methods | Algorithms | Studies | Polynomials | Topological manifolds | Analysis | Optimization | Mathematical programming

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2009, Volume 117, Issue 1, 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 | 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

The Annals of Statistics, ISSN 0090-5364, 4/2016, Volume 44, Issue 2, pp. 813 - 852

In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450...

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Journal Article

Annals of Mathematics and Artificial Intelligence, ISSN 1012-2443, 2/2016, Volume 76, Issue 1, pp. 5 - 23

Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal...

68T05 | 90C26 | Statistical Physics, Dynamical Systems and Complexity | Robotics | Gait optimization | Locomotion | Computer Science | Artificial Intelligence (incl. Robotics) | Mathematics, general | Computer Science, general | Bayesian optimization | 68T40 | 49Mxx | Analysis | Robots

68T05 | 90C26 | Statistical Physics, Dynamical Systems and Complexity | Robotics | Gait optimization | Locomotion | Computer Science | Artificial Intelligence (incl. Robotics) | Mathematics, general | Computer Science, general | Bayesian optimization | 68T40 | 49Mxx | Analysis | Robots

Journal Article

Applied and Computational Harmonic Analysis, ISSN 1063-5203, 03/2016, Volume 40, Issue 2, pp. 417 - 429

Matrix completion involves recovering a matrix from a subset of its entries by utilizing interdependency between the entries, typically through low rank...

Exact line-search | Gradient descent | Alternating minimization | Matrix completion | 68Q25 | 90C26 | 65J20 | 65F10 | MSC 15A29 | 41A29 | MATHEMATICS, APPLIED | FACTORIZATION | Analysis | Methods | Algorithms | State of the art | Computation | Images | Harmonic analysis | Strategy | Mathematical models | Computational efficiency

Exact line-search | Gradient descent | Alternating minimization | Matrix completion | 68Q25 | 90C26 | 65J20 | 65F10 | MSC 15A29 | 41A29 | MATHEMATICS, APPLIED | FACTORIZATION | Analysis | Methods | Algorithms | State of the art | Computation | Images | Harmonic analysis | Strategy | Mathematical models | Computational efficiency

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2019, Volume 19, Issue 6, pp. 1223 - 1263

Consider a finite system of non-strict polynomial inequalities with solution set $$S\subseteq \mathbb R^n$$ S ⊆ R n . Its Lasserre relaxation of degree d is a...

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

52A20 | Positive polynomial | 52A41 | Semidefinitely representable set | Secondary: 12D15 | Mathematics | Moment relaxation | 46L30 | Primary: 13J30 | Linear matrix inequality | Applications of Mathematics | Math Applications in Computer Science | Economics, general | Lasserre relaxation | Spectrahedron | Semidefinite programming | Sum of squares | 14P10 | Linear and Multilinear Algebras, Matrix Theory | 90C26 | Basic closed semialgebraic set | Pure state | Polynomial optimization | Numerical Analysis | 90C22 | Computer Science, general | Approximation theory | Fields, Algebraic | Research | Mathematical research | Mathematical analysis | Polynomials | Hulls (structures) | Linear matrix inequalities | Convexity | Matrix methods | Optimization

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2009, 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 | STABILITY NUMBER | GRAPH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SEMIDEFINITE RELAXATIONS | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 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 | STABILITY NUMBER | GRAPH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SEMIDEFINITE RELAXATIONS | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Management science | Studies | Linear programming | Mathematical programming

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 10/2019, Volume 90, Issue 2, pp. 255 - 270

The aim of this work is to locate a semi-obnoxious facility, i.e. to minimize the distances to a given set of customers in order to save transportation costs...

Obnoxious facility location | Global optimization | 90B85 | 90C46 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Primal and dual algorithms | Mathematics | Dc problems | 90C26 | Business and Management, general | Algorithms

Obnoxious facility location | Global optimization | 90B85 | 90C46 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Primal and dual algorithms | Mathematics | Dc problems | 90C26 | Business and Management, general | Algorithms

Journal Article

The Annals of Statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2164 - 2201

We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly...

Objective functions | Statistical properties | Statistical theories | Least squares | Learning disabilities | Estimators | Perceptron convergence procedure | Logistics | Oracles | Computational statistics | Optimal statistical rate | Nonconvex regularized M-estimation | Geometric computational rate | Path-following method | REGRESSION | PATH | GRADIENT METHODS | geometric computational rate | ALGORITHM | STATISTICS & PROBABILITY | MULTISTAGE CONVEX RELAXATION | GENERALIZED LINEAR-MODELS | VARIABLE SELECTION | NONCONCAVE PENALIZED LIKELIHOOD | path-following method | optimal statistical rate | LASSO | REGULARIZATION | Statistics - Machine Learning | 90C52 | 62F30 | 90C26 | 62J12

Objective functions | Statistical properties | Statistical theories | Least squares | Learning disabilities | Estimators | Perceptron convergence procedure | Logistics | Oracles | Computational statistics | Optimal statistical rate | Nonconvex regularized M-estimation | Geometric computational rate | Path-following method | REGRESSION | PATH | GRADIENT METHODS | geometric computational rate | ALGORITHM | STATISTICS & PROBABILITY | MULTISTAGE CONVEX RELAXATION | GENERALIZED LINEAR-MODELS | VARIABLE SELECTION | NONCONCAVE PENALIZED LIKELIHOOD | path-following method | optimal statistical rate | LASSO | REGULARIZATION | Statistics - Machine Learning | 90C52 | 62F30 | 90C26 | 62J12

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, 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 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | CONVEX | ALGORITHMS | ALTERNATING PROJECTIONS | CONVERGENCE RATE | 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 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | CONVEX | ALGORITHMS | ALTERNATING PROJECTIONS | CONVERGENCE RATE | Studies | Mathematical analysis | Optimization | Convergence | Mathematical programming | Splitting | Thresholds | Direct reduction | Clusters | Mathematical models

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2011, Volume 128, Issue 1, pp. 49 - 72

Many combinatorial constraints over continuous variables such as SOS1 and SOS2 constraints can be interpreted as disjunctive constraints that restrict the...

Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | 90C26 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PIECEWISE-LINEAR OPTIMIZATION | REPRESENTABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FORMULATIONS | COMBINATORIAL OPTIMIZATION | ALGORITHM | CONVEX-HULL | NONCONVEX | INTEGER PROGRAMMING-MODELS | BRANCH-AND-CUT | Studies | Graphs | Mathematical analysis | Mixed integer | Polyhedra | Polyhedrons | Mathematical models | Tightness | Combinatorial analysis | Unions

Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | 90C26 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PIECEWISE-LINEAR OPTIMIZATION | REPRESENTABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FORMULATIONS | COMBINATORIAL OPTIMIZATION | ALGORITHM | CONVEX-HULL | NONCONVEX | INTEGER PROGRAMMING-MODELS | BRANCH-AND-CUT | Studies | Graphs | Mathematical analysis | Mixed integer | Polyhedra | Polyhedrons | Mathematical models | Tightness | Combinatorial analysis | Unions

Journal Article

Mathematical Programming, ISSN 0025-5610, 8/2014, Volume 146, Issue 1, pp. 97 - 121

Lasserre’s hierarchy is a sequence of semidefinite relaxations for solving polynomial optimization problems globally. This paper studies the relationship...

Semidefinite program | 65K05 | Theoretical, Mathematical and Computational Physics | Sum of squares | Mathematics | 90C26 | Lasserre’s hierarchy | Optimality conditions | Mathematical Methods in Physics | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | Combinatorics | Lasserre's hierarchy | MATHEMATICS, APPLIED | REPRESENTATIONS | DEGREE BOUNDS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NONNEGATIVE POLYNOMIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GLOBAL OPTIMIZATION | SQUARES | Studies | Semidefinite programming | Polynomials | Analysis | Optimization | Mathematical programming | Hierarchies | Mathematical analysis | Boundaries | Nonlinear programming | Standards | Convergence

Semidefinite program | 65K05 | Theoretical, Mathematical and Computational Physics | Sum of squares | Mathematics | 90C26 | Lasserre’s hierarchy | Optimality conditions | Mathematical Methods in Physics | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | Combinatorics | Lasserre's hierarchy | MATHEMATICS, APPLIED | REPRESENTATIONS | DEGREE BOUNDS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NONNEGATIVE POLYNOMIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GLOBAL OPTIMIZATION | SQUARES | Studies | Semidefinite programming | Polynomials | Analysis | Optimization | Mathematical programming | Hierarchies | Mathematical analysis | Boundaries | Nonlinear programming | Standards | Convergence

Journal Article

Mathematical Programming, ISSN 0025-5610, 1/2009, Volume 116, Issue 1, pp. 5 - 16

We study the convergence of the proximal algorithm applied to nonsmooth functions that satisfy the Łjasiewicz inequality around their generalized critical...

Mathematical and Computational Physics | Mathematics | 90C26 | Łjasiewicz inequality | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Proximal algorithm | Subanalytic functions | Combinatorics | 47N10 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | proximal algorithm | THEOREM | subanalytic functions | Lujasiewicz inequality | OPTIMIZATION | POINT ALGORITHM | Algorithms | Studies | Mathematical programming

Mathematical and Computational Physics | Mathematics | 90C26 | Łjasiewicz inequality | Mathematical Methods in Physics | 90C30 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Proximal algorithm | Subanalytic functions | Combinatorics | 47N10 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | proximal algorithm | THEOREM | subanalytic functions | Lujasiewicz inequality | OPTIMIZATION | POINT ALGORITHM | Algorithms | Studies | Mathematical programming

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2016, Volume 168, Issue 1, pp. 129 - 152

It is well known that nonlinear conjugate gradient methods are very effective for large-scale smooth optimization problems. However, their efficiency has not...

Nonsmooth | Nonlinear equations | Global convergence | 65K05 | Mathematics | Theory of Computation | 90C26 | Optimization | Calculus of Variations and Optimal Control; Optimization | Conjugate gradient | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Large scale | LINE SEARCH | MATHEMATICS, APPLIED | CONVERGENCE PROPERTIES | SUFFICIENT DESCENT PROPERTY | BUNDLE METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DERIVATIVE-FREE METHOD | BFGS METHOD | PROJECTION METHOD | NEWTON METHOD | TRUST-REGION METHOD | Yuan (China) | Algorithms | Studies | Convex analysis | Conjugate gradient method | Searching | Conjugate gradients | Mathematical models | Convergence

Nonsmooth | Nonlinear equations | Global convergence | 65K05 | Mathematics | Theory of Computation | 90C26 | Optimization | Calculus of Variations and Optimal Control; Optimization | Conjugate gradient | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Large scale | LINE SEARCH | MATHEMATICS, APPLIED | CONVERGENCE PROPERTIES | SUFFICIENT DESCENT PROPERTY | BUNDLE METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DERIVATIVE-FREE METHOD | BFGS METHOD | PROJECTION METHOD | NEWTON METHOD | TRUST-REGION METHOD | Yuan (China) | Algorithms | Studies | Convex analysis | Conjugate gradient method | Searching | Conjugate gradients | Mathematical models | Convergence

Journal Article