摘要
The convergence of the entropy function method for convex nonlinear min-maxproblems is proved. By analyzing the eigenvalue structure of the Hessian matrix,it is found that for high values of the approximation controlling parameter c thedifferentiable optimization problem involved in the entropy function method becomes ill-conditioned and hence difficult to solve. Furthermore, it is shown thatthe entropy function method is indeed equivalent to the simple exponential penaltymethod and hence can be further discussed in the framework of penalty functionmethods. Based on this discovery, in the convex case, it is proved that the entropyfunction method involving Lagrange multiplier (i.e. exponential multiplier penaltymethod) is convergence for ally finite parameter c and hence the ill-condition encountered in the original method can be completely avoided.
The convergence of the entropy function method for convex nonlinear min-maxproblems is proved. By analyzing the eigenvalue structure of the Hessian matrix,it is found that for high values of the approximation controlling parameter c thedifferentiable optimization problem involved in the entropy function method becomes ill-conditioned and hence difficult to solve. Furthermore, it is shown thatthe entropy function method is indeed equivalent to the simple exponential penaltymethod and hence can be further discussed in the framework of penalty functionmethods. Based on this discovery, in the convex case, it is proved that the entropyfunction method involving Lagrange multiplier (i.e. exponential multiplier penaltymethod) is convergence for ally finite parameter c and hence the ill-condition encountered in the original method can be completely avoided.
出处
《计算数学》
CSCD
北大核心
1999年第4期397-406,共10页
Mathematica Numerica Sinica
基金
国家自然科学基金!19701016
内蒙古自然科学基金!9610E16
关键词
熵函数方法
极大极小问题
不可微规划
数学理论
eotropy function method, exponential penalty function,min-max problem, nondifferentiable optimization
