Abstract
In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.
Highlights
IntroductionTrust region algorithm is one of the most often used methods for solving the unconstrained optimization problem min f x
Trust region algorithm is one of the most often used methods for solving the unconstrained optimization problem min f x . (1) x RnGenerally, a trial step is calculated by solving the trust region subproblem min d Rn gkT d dT Bk d k d (2)s.t. d k, 2-norm.Trust region algorithms are blessed with both strong theoretical convergence properties and effectiveness in practice[1,2,3,4]
We present a new line search and trust region algorithm for unconstrained optimization problems
Summary
Trust region algorithm is one of the most often used methods for solving the unconstrained optimization problem min f x . Trust region algorithms are blessed with both strong theoretical convergence properties and effectiveness in practice[1,2,3,4]. It has been studied by many researchers. In 2003, based on the traditional trust region algorithm, Ma [5] proposed a new trust region algorithm, whose trust region radius is k gk and whose trust region center is xk k gk. After carefully studying the idea of traditional trust region algorithms and Ma [5], Zhou et al [6] proposed an improved trust region based on an algorithm depicted in [7]
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