Numerical Study On The Methods For Solving Nonlinear Optimization Problems

In this thesis, some important algorithms for solving nonlinear optimization problems are studied and their practical performance is analyzed by comparing numerical results of some typical testing-functions.The numerical results show the superiority of the conjugate gradient methods. Recent years, the improvements of such algorithms has been mainly studied by experts and scholars, which includes the improvement of parameterβk and step-length ak.The numerical analysis of the important methods which is generalized and summarized is very useful to the practical applications and theoretical research.The methods of punishment functions are introduced in the fourth chapter, In addi-tion, the combination of the methods the conjugate gradient are applied to some optimiza-tion problems with Box-constraint.