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
On the nonmonotone line search
Journal of Optimization Theory and Applications
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
Estimation of optical parameters of very thin films
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Constructing fair curves and surfaces with a Sobolev gradient method
Computer Aided Geometric Design
Convergence properties of nonmonotone spectral projected gradient methods
Journal of Computational and Applied Mathematics
Implicit and adaptive inverse preconditioned gradient methods for nonlinear problems
Applied Numerical Mathematics
Gradient Methods with Adaptive Step-Sizes
Computational Optimization and Applications
Spectral gradient projection method for solving nonlinear monotone equations
Journal of Computational and Applied Mathematics
Spectral projected subgradient with a momentum term for the Lagrangean dual approach
Computers and Operations Research
Memory gradient method with Goldstein line search
Computers & Mathematics with Applications
Nonmonotone derivative-free methods for nonlinear equations
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Convergence of supermemory gradient method
Journal of Applied Mathematics and Computing
Scaled conjugate gradient algorithms for unconstrained optimization
Computational Optimization and Applications
Nonmonotone projected gradient methods based on barrier and Euclidean distances
Computational Optimization and Applications
Computational Optimization and Applications
A derivative-free nonmonotone line-search technique for unconstrained optimization
Journal of Computational and Applied Mathematics
Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization
Optimization Methods & Software
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method
Applied Numerical Mathematics
Convergence of memory gradient methods
International Journal of Computer Mathematics
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
Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization
Journal of Computational and Applied Mathematics
A new family of conjugate gradient methods
Journal of Computational and Applied Mathematics
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
Computational Optimization and Applications
Spectral gradient projection method for monotone nonlinear equations with convex constraints
Applied Numerical Mathematics
Implicit and adaptive inverse preconditioned gradient methods for nonlinear problems
Applied Numerical Mathematics
A new nonmonotone trust-region method of conic model for solving unconstrained optimization
Journal of Computational and Applied Mathematics
Acceleration of the EM algorithm via extrapolation methods: Review, comparison and new methods
Computational Statistics & Data Analysis
Convergence properties of nonmonotone spectral projected gradient methods
Journal of Computational and Applied Mathematics
Notes on the Dai-Yuan-Yuan modified spectral gradient method
Journal of Computational and Applied Mathematics
A multivariate spectral projected gradient method for bound constrained optimization
Journal of Computational and Applied Mathematics
Modified nonmonotone Armijo line search for descent method
Numerical Algorithms
A box constrained gradient projection algorithm for compressed sensing
Signal Processing
Applying Powell's symmetrical technique to conjugate gradient methods
Computational Optimization and Applications
Heterogeneous information integration in hierarchical text classification
PAKDD'06 Proceedings of the 10th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining
Expert Systems with Applications: An International Journal
Journal of Computational and Applied Mathematics
A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand
Computational Optimization and Applications
Limited memory BFGS method with backtracking for symmetric nonlinear equations
Mathematical and Computer Modelling: An International Journal
SPF-GMKL: generalized multiple kernel learning with a million kernels
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
A hybrid ODE-based method for unconstrained optimization problems
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Nonlinear least squares and Sobolev gradients
Applied Numerical Mathematics
Computational Optimization and Applications
A Dynamical Tikhonov Regularization for Solving Ill-posed Linear Algebraic Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
A gradient method for unconstrained optimization in noisy environment
Applied Numerical Mathematics
Two modified scaled nonlinear conjugate gradient methods
Journal of Computational and Applied Mathematics
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The Barzilai and Borwein gradient method for the solution of large scale unconstrained minimization problems is considered. This method requires few storage locations and very inexpensive computations. Furthermore, it does not guarantee descent in the objective function and no line search is required. Recently, the global convergence for the convex quadratic case has been established. However, for the nonquadratic case, the method needs to be incorporated in a globalization scheme. In this work, a nonmonotone line search strategy that guarantees global convergence is combined with the Barzilai and Borwein method. This strategy is based on the nonmonotone line search technique proposed by Grippo, Lampariello, and Lucidi [SIAM J. Numer. Anal., 23 (1986), pp. 707--716]. Numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented. These results indicate that the global Barzilai and Borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations.