摘要
牛顿方法是解决最优化问题的重要方法,牛顿法最突出的优点是收敛速度快.牛顿方向是将目标函数用当前迭代点的二次泰勒多项式近似代替而指向该二次函数极小点的方向,当目标函数本身为二次时,牛顿方向将直指极小点.针对二次函数,我们在本文中从另一个角度给出牛顿方向在几何上的一个新解释,这更加深了我们对牛顿法的认识.
Newton algorithm is an important method to solve the optimization problem,and the most prominent advantages of this algorithm is fast convergence rate.Newton＇s direction is the direction which points to the minimum point of the secondary Taylor polynomial of the objective function with respect to current iteration point.When the objective function is quadratic function itself,Newton＇s direction will directly point to the minimum point of objective function.In this paper,we give a new geometric explanation of Newton＇s direction according to quadratic function from another angle,the further understanding of the Newton algorithm we will know.
出处
《西南民族大学学报（自然科学版）》
CAS
2012年第1期59-63,共5页
Journal of Southwest Minzu University(Natural Science Edition)
基金
国家自然科学基金项目(NO.10901004)资助
宁夏回族自治区精品课程<运筹学>建设项目资助
关键词
最优化问题
牛顿法
新解释
optimization problem
Newton algorithm
new explanation
