An affine-scaling derivative-free trust-region method for solving nonlinear systems subject to linear inequality constraints

• Published in: International journal of computer mathematics Vol. 92; no. 8; pp. 1660 - 1687
• Main Authors: Wang, Peng, Zhu, Detong
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.08.2015; Taylor & Francis Ltd
• Subjects: Algorithms; Backtracking; Construction; Convergence; derivative-free optimization; Dynamical systems; interior point; Interpolation; Mathematical analysis; Mathematical models; Mathematical problems; Nonlinear dynamics; Nonlinear systems; Searching; system of nonlinear equations; trust-region
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2014.959942

In this paper, an affine-scaling derivative-free trust-region method with interior backtracking line search technique is considered for solving nonlinear systems subject to linear inequality constraints. The proposed algorithm is designed to take advantage of the problem structured by building polynomial interpolation models for each function in the nonlinear system function F. The proposed approach is developed by forming a quadratic model with an appropriate quadratic function and scaling matrix: there is no need to handle the constraints explicitly. By using both trust-region strategy and interior backing line search technique, each iteration switches to backtracking step generated by the trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. Under reasonable conditions, the global convergence and fast local convergence rate of the proposed algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.