熵函数法的数学理论

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.