A new trust region method for unconstrained optimization

• Published in: Journal of computational and applied mathematics Vol. 213; no. 2; pp. 509 - 520
• Main Authors: Shi, Zhen-Jun, Guo, Jin-Hua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2008; Elsevier
• Subjects: Acceleration of convergence; Calculus of variations and optimal control; Convergence rate; Exact sciences and technology; Global convergence; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Sciences and techniques of general use; Trust region method; Unconstrained optimization; Global convergence; 90C30; 65K05; Unconstrained optimization; Convergence rate; 49M37; Trust region method; Strong convergence; Unconstrained optimization; Trust region method; Global convergence; Convergence rate; Numerical analysis; Convergence acceleration; Applied mathematics; 90C30; 49M37; 65K05; Optimization method; Iteration; Mathematical programming
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2007.01.027

In this paper, we propose a new trust region method for unconstrained optimization problems. The new trust region method can automatically adjust the trust region radius of related subproblems at each iteration and has strong global convergence under some mild conditions. We also analyze the global linear convergence, local superlinear and quadratic convergence rate of the new method. Numerical results show that the new trust region method is available and efficient in practical computation.