Journal of Optimization Theory and Applications
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Representations of quasi-Newton matrices and their use in limited memory methods
Mathematical Programming: Series A and B
Trust Region Algorithms and Timestep Selection
SIAM Journal on Numerical Analysis
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
A quasi-Newton trust-region method
Mathematical Programming: Series A and B
The convergence of subspace trust region methods
Journal of Computational and Applied Mathematics
An ODE-based trust region method for unconstrained optimization problems
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
This paper presents a hybrid ODE-based method for unconstrained optimization problems, which combines the idea of IMPBOT with the subspace technique and a fixed step-length. The main characteristic of this method is that at each iteration, a lower dimensional system of linear equations is solved only once to obtain a trial step. Another is that when a trial step is not accepted, this proposed method uses minimization of a convex overestimation, thus avoiding performing a line search to compute a step-length. Under some reasonable assumptions, the method is proven to be globally convergent. Numerical results show the efficiency of this proposed method in practical computations, especially for solving small scale unconstrained optimization problems.