基于BFGS算法的广义Lagrange乘子法研究

Research on Generalized Lagrange Multiplier Method based on BFGS Algorithm

广义Lagrange乘子法是解决约束优化的问题的一种重要方法,基于BFGS算法,利用MATLAB工具,研究了初始点的选取、罚因子的改变及罚因子修正系数的改变对该算法收敛效果的影响。结果表明:(1)对于初始点的选取,应尽量在最优点附近进行取值,才能有不错的收敛效果。(2)罚因子过小或过大都对算法求解问题产生困难。如果罚因子太小,大量的搜索时间将花费在非可行域,使迭代次数增加。另一方面,如果罚因子过大,算法将很难被推进到可行域以内,导致算法收敛失败。(3)随着罚因子修正系数的变化,随时会出现无法收敛的现象,故该系数的值应在迭代成功率相对较高的分段选取。

The generalized Lagrange multiplier method is an important method to solve the problem of constrained optimi-zation.Based on BFGS algorithm,this paper uses MATLAB tool to study the influnence of initial point selection,penalty factor change and penalty factor change correction coefficient.The results show that:(1)For the selection of the initial point,the value should be selceted near the best point,and the convergence effect can be good.(2)The penalty factor too small or too large will make the algorithm difficult to solve.If the penalty factor is too small,a large amount of search time will cost in the non-feasible domain,which will increases the number of iterations.On the other hand,if the penal-ty factor is too large,the algorithm will be difficult to be pushed into the feasible domain,which will causes the algo-rithm fail to converge.(3)With the change of the penalty factor correction coefficient,there is a phenomenon of fail to converge at any time.Therefore,the value of the coefficient is supposed to selct during the segment of iteration success rate that is relatively high.