Year: 2018
Author: Caixia Kou, Zhongwen Chen, Yuhong Dai, Haifei Han
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 331–350
Abstract
An augmented Lagrangian trust region method with a bi-object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1705-m2016-0820
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 331–350
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence.