Using truncated conjugate gradient method in trust-region method with two subproblems and backtracking line search

Abstract

Abstract.A trust-region method with two subproblems and backtracking line search for solving unconstrained optimization is proposed. At every iteration, we use the truncated conjugate gradient method or its variation to solve one of the two subproblems approximately. Backtracking line search is carried out when the trust-region trail step fails. We show that this method have the same convergence properties as the traditional trust-region method based on the truncated conjugate gradient method. Numerical results show that this method is as reliable as the traditional one and more efficient in respect of iterations, CPU time and evaluations. Mathematical subject classification: Primary: 65K05; Secondary: 90C30.

A Fourth-Order Nonlinear Conjugate Gradient Method in Equality Constrained Optimization

“…and Many of these conjugate gradient methods use inexact line search technique [21]. Others use exact line search approach [22].…”

Trust region algorithm with two subproblems for bound constrained problems

“…In the previous research [10], we proposed a trust region algorithm with two subproblems for unconstrained problems. A subproblem without trust region constraint is introduced into the trust region framework in order to use the Newton step.…”