解新锥模型信赖域子问题的折线法  

A Dogleg Method for Solving New Trust-region Subproblems of Conic Model

作　　者：陆晓平[1] 倪勤[2] 刘浩[3] 

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]南京航空航天大学理学院,南京210016 [3]南京工业大学理学院,南京210009

出　　处：《应用数学学报》2007年第5期855-871,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10471062);江苏省基础研究计划(自然科学基金;BK2006184)资助项目.

摘　　要：本文以新锥模型信赖域子问题的最优性条件为理论基础,认真讨论了新子问题的锥函数性质,分析了此函数在梯度方向及与牛顿方向连线上的单调性.在此基础上本文提出了一个求解新锥模型信赖域子问题折线法,并证明了这一子算法保证解无约束优化问题信赖域法全局收敛性要满足的下降条件.本文获得的数值实验表明该算法是有效的.Based on the optimality conditions of new conic model trust-region subproblem proposed in [8], we discuss the properties of conic function of new subproblem, and analyze the monotonicity of conic function in the gradient or in the line section between gradient and Newton＇s direction. According to this theory a dogleg algorithm for solving new trust-region subproblems of conic model is proposed in this paper. We proved the descent condition of this algorithm which guaranteed the global convergence of trust-region method for solving unconstrained optimization problem. The numerical experiment shows that this algorithm is efficient.

关 键 词：无约束最优化 锥模型 信赖域子问题 

分 类 号：O221.2[理学—运筹学与控制论]