A smoothing self-adaptive Levenberg-Marquardt algorithm for solving system of nonlinear inequalities

作者：He, Chan; Ma, Changfeng^*

来源：Applied Mathematics and Computation, 2010, 216(10): 3056-3063.

DOI：10.1016/j.amc.2010.04.025

• Nonlinear inequalities
• Smoothing self-adaptive Levenberg-Marquardt algorithm
• Global convergence
• Local quadratic convergence

In this paper, we consider the smoothing self-adaptive Levenberg-Marquardt algorithm for the system of nonlinear inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations H(x) = 0. A smoothing self-adaptive Levenberg-Marquardt algorithm is proposed for solving the system of nonlinear inequalities based on the new smoothing function. The Levenberg-Marquardt parameter mu(k) is chosen as the product of mu(k) = parallel to H-k parallel to(delta) with delta(2) is an element of (0,2] being a positive constant. We will show that if parallel to H-k parallel to(delta) provides a local error bound, which is weaker than the non-singularity, the proposed method converges superlinearly to the solution for delta is an element of (0,1), while quadratically for delta is an element of [1,2]. Numerical results show that the new method performs very well for system of inequalities.

• 出版日期2010-7-15
• 单位福建师范大学; 桂林电子科技大学; 五邑大学