Nonmonotone Spectral Projected Gradient Methods on Convex Sets
Top Cited Papers
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 10 (4), 1196-1211
- https://doi.org/10.1137/s1052623497330963
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 presentedKeywords
This publication has 24 references indexed in Scilit:
- Restricted optimization: a clue to a fast and accurate implementation of the Common Reflection Surface Stack methodJournal of Applied Geophysics, 1999
- Estimation of the Optical Constants and the Thickness of Thin Films Using Unconstrained OptimizationJournal of Computational Physics, 1999
- Automatic differentiation and spectral projected gradient methods for optimal control problemsOptimization Methods and Software, 1998
- A new trust region algorithm for bound constrained minimizationApplied Mathematics & Optimization, 1994
- On the Barzilai and Borwein choice of steplength for the gradient methodIMA Journal of Numerical Analysis, 1993
- A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple BoundsSIAM Journal on Numerical Analysis, 1991
- Two-Point Step Size Gradient MethodsIMA Journal of Numerical Analysis, 1988
- On the Goldstein-Levitin-Polyak gradient projection methodIEEE Transactions on Automatic Control, 1976
- Constrained minimization methodsUSSR Computational Mathematics and Mathematical Physics, 1966
- Convex programming in Hilbert spaceBulletin of the American Mathematical Society, 1964