A filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

作     者：Pei, Yonggang Song, Shaofang Zhu, Detong 

作者机构：Henan Normal Univ Coll Math & Informat Sci Engn Lab Big Data Stat Anal & Optimal Control Construct Rd Xinxiang 453007 Henan Peoples R China Shanghai Normal Univ Math & Sci Coll Guilin Rd Shanghai 200234 Peoples R China 

出 版 物：《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期：2023年第93卷第4期

页      面：1481-1507页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China Key Scientific Research Project for Colleges and Universities in Henan Province 21A110012 

主　　题：Nonlinear constrained optimization Cubic regularization Filter methods Sequential quadratic programming Global convergence 

摘      要：In this paper, we propose a filter sequential adaptive regularization algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with linearized constraints is considered to obtain a trial step in each iteration. Composite step methods and reduced Hessian methods are employed to tackle the linearized constraints. As a result, a trial step is decomposed into the sum of a normal step and a tangential step which is computed by a standard ARC subproblem. Then, the new iteration is determined by filter methods and ARC framework. The global convergence of the algorithm is proved under some reasonable assumptions. Preliminary numerical experiments and comparison results are reported.