Some Algorithms For Optimization Problems

This thesis is devoted to some numerical methods ,such as entropy method, filled function method and homotopy method. Their properties and extended applications are discussed on emphasis. The main work of the dissertation can be summarized as follows:Essential properties of the adjusted maximum entropy function and the convergence analysis of the method are investigated at fist. Then the effectivity of the method is illustrated by using to solve the general constrained optimization problems and the multi-objective problem .Furthermore ,an extended dual algorithm is described. Finally,numerical results are given and analyzed.Some new extension and applications of the homotopy method are discussed. First, an continued homotopy method ,based on the entropy function ,is applied to solve the multi-objective problem. Then an path following method on the basis of the entropy function is applied to solve nonlinear equations .Theory analysis and numerical experiments show that the method is effective.Besides all of the above ,a new modified filled function method is given to solve the Lipschitz problem ,and the convergence analysis and the numerical results show this new method is practical and effective.