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.
出处
《应用数学学报》
CSCD
北大核心
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.
关键词
无约束最优化
锥模型
信赖域子问题
unconstrained minimization
conic model
trust region subproblem
