摘要
对于增广拉格朗日乘子法,分析表明其解析解只有一个不等式约束的边界解严格成立,而其在可行域内的解析解在松弛变量为实数时存在,当松弛变量为虚数时不等式约束不满足,解析解不在可行域内,增广拉格朗日乘子法无效。当采用无约束最优化算法求解数值解时,在一定的条件下数值解在可行域内,增广拉格朗日乘子法有效,若条件不成立,则增广拉格朗日乘子法无效。本文在增广拉格朗日函数中加入松弛因子,修正了增广拉格朗日乘子法,使其具有一个在可行域内的严格成立的解析解,当松弛因子与终止条件的允许误差限满足一定的条件时,不等式约束满足,修正增广拉格朗日乘子法严格成立。数值分析实例验证了上述研究的有效性。
In the light of ugmented lagrange multiplier technique,an analysis indicates that the analytical solution along its boundary is strictly established under only one unequal constraint. Its analytical solution is located in its feasible region under real number slack variable. Otherwise the analytical solution is located outside its feasible region under imaginary number slack variable,and unequal constraint no-satisfying,so that ugmented lagrange multiplier technique is not valid. As using unconstrained optimization algorithm,numerical solution obtained is located in feasible region under some special conditions. ugmented lagrange multiplier technique is valid. But if the condition is not sufficient,it is not valid. Adding slack factor into augmented lagrangian function,a modifying augmented lagrange multiplier technique was developed,its analytical solution inside feasible region is strictly established. As the slack factor and the admission error restriction of ending condition as well as unequal constraint satisfaction,the modifying augmented lagrange multiplier technique is strictly established. Results of numerical analysis verify the validity of the technique.
作者
侯小秋
HOU Xiaoqiu(School of Electronics and Controlling Engineering,Heilongjiang University of Science Technology,Haerbin 150022,China)
出处
《中央民族大学学报（自然科学版）》
2021年第3期9-15,92,共8页
Journal of Minzu University of China(Natural Sciences Edition)
关键词
增广拉格朗日乘子法
松弛变量
增广拉格朗日函数
松弛因子
允许误差限
augmented Lagrange multiplier technique
feasible region
slack variable
augmented Lagrangian function
slack factor
admission error restriction
作者简介
侯小秋(1965-),男(汉族),黑龙江省双城人,黑龙江科技大学电气与控制工程学院副教授,主要研究方向:非线性控制、预测控制、自适应控制、智能PID控制。
