Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Authors:
Ernesto G. Birgin;José Mario Martínez;Marcos Raydan
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
1999

Citing 0
Cited 68

Algorithm 813: SPG—Software for Convex-Constrained Optimization

ACM Transactions on Mathematical Software (TOMS)
Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization

Computational Optimization and Applications
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients

Computational Optimization and Applications
Optimization problems in the estimation of parameters of thin films and the elimination of the influence of the substrate

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems

Computational Optimization and Applications
Convergence properties of nonmonotone spectral projected gradient methods

Journal of Computational and Applied Mathematics
Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization

Computers and Operations Research
Gradient Methods with Adaptive Step-Sizes

Computational Optimization and Applications
Spectral projected subgradient with a momentum term for the Lagrangean dual approach

Computers and Operations Research
Parallel Software for Training Large Scale Support Vector Machines on Multiprocessor Systems

The Journal of Machine Learning Research
Minimizing the object dimensions in circle and sphere packing problems

Computers and Operations Research
Nonmonotone projected gradient methods based on barrier and Euclidean distances

Computational Optimization and Applications
Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Computational Optimization and Applications
Quasi-Newton acceleration for equality-constrained minimization

Computational Optimization and Applications
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method

Applied Numerical Mathematics
Deterministic Defuzzification Based on Spectral Projected Gradient Optimization

Proceedings of the 30th DAGM symposium on Pattern Recognition
Improving ultimate convergence of an augmented Lagrangian method

Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Solving the quadratic trust-region subproblem in a low-memory BFGS framework

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Spatiotemporal Decomposition in Object-Space along Reconstruction in Emission Tomography

MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
A globally convergent BFGS method with nonmonotone line search for non-convex minimization

Journal of Computational and Applied Mathematics
Hybrid spectral gradient method for the unconstrained minimization problem

Journal of Global Optimization
Structure learning of Bayesian networks using constraints

ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Spectral gradient projection method for monotone nonlinear equations with convex constraints

Applied Numerical Mathematics
On Nonmonotone Chambolle Gradient Projection Algorithms for Total Variation Image Restoration

Journal of Mathematical Imaging and Vision
Sparse reconstruction by separable approximation

IEEE Transactions on Signal Processing
Convergence properties of nonmonotone spectral projected gradient methods

Journal of Computational and Applied Mathematics
Second-order negative-curvature methods for box-constrained and general constrained optimization

Computational Optimization and Applications
Multi-objective Pareto-optimal control: an application to wastewater management

Computational Optimization and Applications
Notes on the Dai-Yuan-Yuan modified spectral gradient method

Journal of Computational and Applied Mathematics
Continuous GRASP with a local active-set method for bound-constrained global optimization

Journal of Global Optimization
Orthogonal packing of identical rectangles within isotropic convex regions

Computers and Industrial Engineering
Duality-based algorithms for total-variation-regularized image restoration

Computational Optimization and Applications
A multivariate spectral projected gradient method for bound constrained optimization

Journal of Computational and Applied Mathematics
Topology Selection in Graphical Models of Autoregressive Processes

The Journal of Machine Learning Research
Adaptive First-Order Methods for General Sparse Inverse Covariance Selection

SIAM Journal on Matrix Analysis and Applications
Model-Based Multiple Rigid Object Detection and Registration in Unstructured Range Data

International Journal of Computer Vision
Convex constrained optimization for large-scale generalized Sylvester equations

Computational Optimization and Applications
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping

Computers and Graphics
Fast Projections onto l1,q-norm balls for grouped feature selection

ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Generalized dictionary learning for symmetric positive definite matrices with application to nearest neighbor retrieval

ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
A projected---gradient interior---point algorithm for complementarity problems

Numerical Algorithms
Uni-orthogonal nonnegative tucker decomposition for supervised image classification

ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Block relaxation and majorization methods for the nearest correlation matrix with factor structure

Computational Optimization and Applications
Shape optimization for tumor location

Computers & Mathematics with Applications
Computing a Nearest Correlation Matrix with Factor Structure

SIAM Journal on Matrix Analysis and Applications
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery

SIAM Journal on Imaging Sciences
An Affine-Scaling Interior-Point Method for Continuous Knapsack Constraints with Application to Support Vector Machines

SIAM Journal on Optimization
Coverage segmentation based on linear unmixing and minimization of perimeter and boundary thickness

Pattern Recognition Letters
Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea

Expert Systems with Applications: An International Journal
A restrained optimal perturbation method for solving the inverse problem in reverse process of convection diffusion equation

ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
A modified conjugate gradient algorithm with cyclic Barzilai-Borwein steplength for unconstrained optimization

Journal of Computational and Applied Mathematics
A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

Computational Optimization and Applications
Non-monotone projection gradient method for non-negative matrix factorization

Computational Optimization and Applications
SCIHTBB: Sparsity constrained iterative hard thresholding with Barzilai-Borwein step size

Neurocomputing
SPF-GMKL: generalized multiple kernel learning with a million kernels

Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Minimizing Condition Number via Convex Programming

SIAM Journal on Matrix Analysis and Applications
Co-Segmentation of 3D Shapes via Subspace Clustering

Computer Graphics Forum
Low-rank mechanism: optimizing batch queries under differential privacy

Proceedings of the VLDB Endowment
Evaluating bound-constrained minimization software

Computational Optimization and Applications
Loss-specific training of non-parametric image restoration models: a new state of the art

ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems

Computational Optimization and Applications
A cyclic projected gradient method

Computational Optimization and Applications
Linear convergence analysis of the use of gradient projection methods on total variation problems

Computational Optimization and Applications
Assessing the Value of Dynamic Pricing in Network Revenue Management

INFORMS Journal on Computing
Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization

Computational Optimization and Applications
ParNes: a rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals

Numerical Algorithms
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

Journal of Global Optimization
An active set truncated Newton method for large-scale bound constrained optimization

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.01

Visualization

Abstract

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.