A nonmonotone quasi-Newton trust-region method of conic model for unconstrained optimization

Authors:
Shao-Jian Qu;Qing-Pu Zhang;Su-Da Jiang
Affiliations:
School of Management, Harbin Institute of Technology, Harbin, China,Natural Science Research Centre, Harbin Institute of Technology, Harbin, China;School of Management, Harbin Institute of Technology, Harbin, China;Engineering Department, Huawei Institute of Technology, Nanjing, China
Venue:
Optimization Methods & Software
Year:
2009

Citing 6
Cited 0

A nonmonotone line search technique for Newton's method

SIAM Journal on Numerical Analysis
Deriving collinear scaling algorithms as extension of quasi-Newton methods and the local convergence of DFP-and BFGS-related collinear scaling algorithms

Mathematical Programming: Series A and B
Nonmonotone trust region methods with curvilinear path in unconstrained optimization

Computing
An assessment of nonmonotone linesearch techniques for unconstrained optimization

SIAM Journal on Scientific Computing
Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints

Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a new nonmonotone quasi-Newton trust-region algorithm of the conic model for the solution of unconstrained optimization problems, where the computation of the horizontal vectors is easier and the approximate Hessian matrices can be maintained positive definite. Under reasonable assumptions, the global convergence, the locally linear and superlinear convergence of the proposed algorithm are developed, respectively. It is well known that in applying trust-region algorithms, the basic issue is how to solve the trust-region subproblem efficiently. To deal with the issue, an approximate solution method is developed in this paper. Note that the approximate solution method not only is computationally cheap, but also preserves the strong convergence properties as the exact solution methods. Numerical results are shown for a number of test problems from the literature.