常数拟合二阶偏导数矩阵定点优化方法  

Fixed-point Optimization Method of Constant Fitting Second-order Partial Derivative Matrix

作　　者：李春明[1,2] 刘庆[1] 李万腾 Li Chunming;Liu Qing;Li Wanteng(Shengli College of China University of Petroleum,China University of Petroleum (East China),Dongying 257061,China;School of Mechanical and Electronic Engineering,China University of Petroleum (East China),Qingdao 266580,China;School of Mechanical Engineering,Shandong University,Ji'nan 250061,China)

机构地区：[1]中国石油大学(华东)中国石油大学胜利学院,山东东营257061 [2]中国石油大学(华东)机电工程学院,山东青岛266580 [3]山东大学机械工程学院,山东济南250061

出　　处：《甘肃科学学报》2021年第3期29-34,共6页Journal of Gansu Sciences

基　　金：山东省自然科学基金(Q2006A08)。

摘　　要：在优化方法学科当中,拟合法均具有有效的寻优效果。提出了常数拟合二阶偏导数矩阵法。基于目标函数的单峰假设,在当前点处,由目标函数的梯度和二阶偏导数矩阵拟合具有常数二阶偏导数矩阵的函数。令该函数的极值点为新点继续寻优,直到相邻2个新点足够接近为止。推导了新点的计算公式,给出了寻优步骤和程序流程图。新算法与高次多维二阶近似式拟合函数定点法(经典的多维牛顿法)的求点结果相同,但是基本理念、出发点和算法不同,其计算量更小,也不会因矩阵不可逆而计算失败。二维Rosenbrock函数的算例验证了其寻优有效性。将新算法用于一维优化问题,则可称为常数拟合二阶导数定点法。沿当前点指向新点的方向进行一维寻优,则可称为常数二阶偏导数矩阵方向法。In the optimization methods subject,the fitting method has an effective optimization effect.The fixed-point optimization method of constant fitting second-order partial derivative matrix is proposed.Based on the single peak assumption of objective function,the function with constant second-order partial derivative matrix is fitted by the gradient and second-order partial derivative matrix of objective function at the current point.The extreme point of the function is taken as a new point to search optimization until the two new points are close enough.The calculation formula of the new point is deduced,and the optimization steps and program flow chart are given.The result of the new algorithm are the same as that of the high-order multi-dimensional second-order approximate fitting function fixed-point method(the classical multi-dimensional Newton method).However,the algorithm,basic concept and starting point are different,its computation is less,and it will not fail even if the matrix is irreversible.An example of two-dimensional Rosenbrock function verifies the effectiveness of the new optimization algorithm.When the new algorithm is applied to one-dimensional optimization problems,it can be called the fixed-point optimization method of constant fitting second derivative.If along the direction of the current point pointing to the new point to search by one-dimensional optimization,the algorithm can be called the direction method based on constant second-order partial derivative matrix.

关 键 词：优化方法 拟合法 二阶偏导数矩阵 定点法 单峰假设 

分 类 号：O224[理学—运筹学与控制论] O221[理学—数学]