大规模界约束极小化问题的有效集截断牛顿法

来源期刊：中南大学学报(自然科学版)2002年第1期

论文作者：梁昔明 蔡自兴

文章页码：82 - 86

关键词：大规模界约束极小化问题;有效集截断牛顿法;整体收敛性;数值试验

Key words：large-scale bound constrained minimization; active set truncated-Newton method; global convergence;numerical comparisons

摘    要：许多工业过程的模型可转化为一个大规模界约束极小化问题.作者基于确定最优解处有效集的有效技巧和截断牛顿法,给出了一个求解该类问题的有效集截断牛顿法.该方法在每次迭代中,先启用允许快速修改工作集的估计技巧来估计最优解处的有效约束,然后利用截断牛顿法确定搜索方向对应于自由变量的分量,最后利用Armijo非精确线搜索得可行点;证明了所给方法的整体收敛性,并利用一组大规模测试问题对所给方法进行了数值试验,同时与文献[8]中的子空间有限内存拟牛顿法进行了数值比较,结果表明有效集截断牛顿法不仅稳定和有效,而且适合于大规模界约束极小化问题的求解.

Abstract: Manymodels of industrial process can be transformed into a large-scale nonlinear bound constrained minimization. Based on an efficient identification technique of active set at the solution and on a truncated-Newton method, this paper proposed an active set truncated-Newton algorithm for large-scale nonlinear bound constrained minimization. At each iteration, the algorithm first employs a guessing technique, which permits fast changes in the working set, to predict which bounds are active at the solution. Then a truncated-Newton method is used to determine the components of search direction corresponding to the free variables and an Armijo stabilization technique is employed to obtain a feasible iterative point. The global convergence of the method is proved and the numerical comparisons with the performance of subspace limited memory quasi-Newton algorithm in [8] on a set of large-scale problems are also made.