A trust region method with project step for bound constrained optimization without compact condition

ABSTRACT

In this paper, we propose a trust region method for the solution of the nonlinear optimization problem with bound constraints. The method differs from the existing trust region method in that we use the trust region step as a trial step and the project step as a correction step. We prove that the generated sequence is bounded automatically without the compact assumption and obtain global convergence of the proposed algorithm. Numerical results are given to show the efficiency when combined with suitable quasi-Newton update such as BFGS and Barzilai-Borwein update for the Hessian matrix.

Keywords:

• Trust region method
• bound constraints
• projection step
• quasi-Newton update
• Barzilai-Borwein method
• global convergence

2010 AMS Subject Classifications:

• 65K05
• 90C30

Disclosure statement

The authors declared that they have no conflicts of interest to this work.