A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
On the convergence of projected gradient processes to singular critical points
Journal of Optimization Theory and Applications
A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
On the linear convergence of descent methods for convex essentially smooth minimization
SIAM Journal on Control and Optimization
SIAM Journal on Numerical Analysis
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
Weak sharp minima in mathematical programming
SIAM Journal on Control and Optimization
Family of projected descent methods for optimization problems with simple bounds
Journal of Optimization Theory and Applications
Convergence of the Gradient Projection Method for Generalized Convex Minimization
Computational Optimization and Applications
Two facts on the convergence of the Cauchy algorithm
Journal of Optimization Theory and Applications
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Weak Sharp Solutions of Variational Inequalities
SIAM Journal on Optimization
A multivariate spectral projected gradient method for bound constrained optimization
Journal of Computational and Applied Mathematics
Smoothing SQP algorithm for semismooth equations with box constraints
Computational Optimization and Applications
| Hi-index | 7.29 |
In a recent paper, a nonmonotone spectral projected gradient (SPG) method was introduced by Birgin et al. for the minimization of differentiable functions on closed convex sets and extensive presented results showed that this method was very efficient. In this paper, we give a more comprehensive theoretical analysis of the SPG method. In doing so, we remove various boundedness conditions that are assumed in existing results, such as boundedness from below of f, boundedness of x"k or existence of accumulation point of {x"k}. If @?f(.) is uniformly continuous, we establish the convergence theory of this method and prove that the SPG method forces the sequence of projected gradients to zero. Moreover, we show under appropriate conditions that the SPG method has some encouraging convergence properties, such as the global convergence of the sequence of iterates generated by this method and the finite termination, etc. Therefore, these results show that the SPG method is attractive in theory.