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

Abstract

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.

Keywords:

• derivative-free optimization
• trust-region
• system of nonlinear equations
• interior point

2010 AMS Subject Classifications:

• 49M37
• 65K05
• 90C30
• 90C56

Acknowledgements

The authors gratefully acknowledge the partial supports of the National Science Foundation Grant (11371253) of China.