An algorithm for solving new trust region subproblem with conic model  

作　　者：WANG JianYu NI Qin 

机构地区：[1]Department of Mathematics,Nanjing Xiaozhuang University,Nanjing 211171,China [2]Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

出　　处：《Science China Mathematics》2008年第3期461-473,共13页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China (Grant No.10471062);the Natural Science Foundation of Jiangsu Province (Grant No. BK2006184)

摘　　要：The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.

关 键 词：conic model trust-region subproblem nonconvex problem dual method 49K10 90C30 

分 类 号：O211[理学—概率论与数理统计]