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基于试探方向的无约束优化问题算法研究

Research on Algorithm of Unconstrained Optimization Problems Based on Exploratory Direction

中文摘要英文摘要

随着数学、计算机、金融的领域的飞速发展,最优化数学与我们日常生活密切相关,最优化理论与方法作为一门应用性很强的学科,在日常生活中如何以最优化的方法解决日常生活问题中,是当今数学界面临的热门话题.我们通过对最优化方法这门课的学习,并针对相关问题的研究,在经典的无约束优化问题的算法基础上,提出一种基于多种下降方向的新的迭代算法,并证明了该算法在非精确一维搜索下的全局收敛性,并用数值实例验证实验结果来进一步说明该算法是有效的。

As mathematics, computer and the rapid development of financial field, optimization mathematics is closely related to our daily life, optimization theory and methods as a applied very strong discipline, in daily life how to optimization methods to solve problems in daily life, is a hot topic in today's maths face. We learn through the optimization method of this course, and studies of related issues, in the classical algorithm based on unconstrained optimization problems, in this paper, a new iteration algorithm based on a variety of drop direction, and proves that the algorithm in the global convergence under exact one-dimensional search, a numerical example to verify the experimental results to further illustrate the algorithm is effective.

胡波、刘建飞、邵虎、叶樟源

数学计算技术、计算机技术

信息与计算科学无约束优化最速下降法牛顿法共轭梯度法全局收敛性

Information and computing scienceunconstrained optimizationsteepest descent methodNewton methodconjugate gradient methodglobal convergence

胡波,刘建飞,邵虎,叶樟源.基于试探方向的无约束优化问题算法研究[EB/OL].(2013-12-11)[2025-08-03].http://www.paper.edu.cn/releasepaper/content/201312-228.点此复制

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