【作者】 张乐友；

【导师】 刘三阳；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2002， 硕士

【摘要】 本文针对几种重要的优化模型，对近几年备受关注的几种新型优化算法(如极大熵函数法、同伦算法、填充函数法等)作了比较深入的研究，在此基础上将这些算法有机结合并作了进一步的改进、推广和应用，取得了比较满意的效果，详细内容如下： 1．对熵函数法作了进一步的研究，对改进的熵函数法作了较深入的理论分析，给出了误差估计，并将其用于解一般的约束问题、多目标规划问题，在此基础上又构造了一种新的对偶算法，并给出数值实验和收敛性证明． 2．对同伦算法作了进一步的推广应用，并利用熵函数法思想，给出了多目标规划的一种连续同伦算法，此外对非线性方程组提出了一种路径跟踪算法，理论分析与数值实验表明本算法比其它算法具有更快的收敛速度，且数值稳定性较好． 3．对填充函数法作了较深入的研究，在已有算法的基础上提出了一种单参数填充函数法，理论分析与数值实验表明该算法明显优于已有的算法．更多还原

【Abstract】 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.更多还原