On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure  

作　　者：XUE Dan SUN WenYu 

机构地区：[1]School of Mathematical Sciences,Jiangsu Key Labratory for NSLSCS,Nanjing Normal University

出　　处：《Science China Mathematics》2014年第6期1287-1302,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11071122 and 11171159);the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No. 20103207110002)

摘　　要：In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.In this paper, we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure, where derivatives of the objective function are not available and cannot be directly approximated. At each iteration, we construct a quadratic interpolation model of the objective function around the current iterate. The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region. The filter technique is used to ensure the feasibility and optimality of the iterative sequence. Global convergence of the proposed algorithm is proved under some suitable assumptions.

关 键 词：constrained optimization derivative-free optimization multivariate interpolation separable op-timization global convergence 

分 类 号：O224[理学—运筹学与控制论] TP273.22[理学—数学]