【作者】 李晗；

【导师】 倪勤；

【作者基本信息】 南京航空航天大学 ， 运筹学与控制论， 2006， 硕士

【摘要】 解一般非线性规划问题的移动渐近线(moving asymptotes,以下简称MA)信赖域方法,是一类最新提出的优化方法,主要用于解工程上经常出现的结构优化问题. MA模型具有严格凸和可分的良好特性,以此建立的算法具有全局收敛性质.本文分析了MA模型和信赖域方法的特点,构造了MA模型信赖域子问题,并利用投影梯度法进行求解,在此基础上提出了一个新的求解非线性规划问题的MA(移动渐近线)模型信赖域方法.对方法中MA模型渐近线参数的选择进行了讨论,给出了方法的全局收敛性证明.文章最后给出了数值实验,验证了此方法的可行性.研究结果表明,本文提出的MA模型信赖域方法可能是一种有效的方法.论文的第一章简介了最优化方法和MA模型的基本思想.第二章对一些背景知识如非线性规划、信赖域方法和投影梯度法进行了介绍,提出了用投影梯度法求解MA模型的思路.在第三章建立了一个新的MA模型信赖域子问题,并讨论了它的性质.第四章主要考虑解子问题的投影梯度算法及收敛性质,同时给出一个新的解非线性规划问题的MA模型信赖域方法.第五章是MA模型信赖域方法的收敛性分析,第六章是相应的数值实验.更多还原

【Abstract】 The method of moving asymptotes (MA) with trust region technique is a kind of new optimization method for solving general nonlinear programming problems, especially for structure optimization problem in engineering. The MA model is strict convex and separable, and the algorithm based on this model is globally convergent. In this paper the characters of MA model and the trust region method are analyzed, a subproblem with MA model and trust region technique is presented, and a projected gradient method is used to solve the subproblem. Based on these results we proposed a new trust region method with MA model for solving nonlinear programming problems. We discuss how to design the MA model and its parameters in this method and prove the global convergence of this method. In addition, we carry out some numerical tests for this method. It can be concluded from these results that the trust region method with MA model is efficient.In Chapter one, basic theories of optimization method and MA model are introduced. The backgrounds of nonlinear programming, trust-region method as well as projected gradient method are illustrated in the following chapter. Then it also gives the general ideas of methods for solving MA model with projected gradient method. In Chapter three, a new projected gradient method for solving MA model is given. It can deal with general nonlinear programming with trust region technique. The important properties of the improved model are analyzed and the algorithm is proposed, too. After that a MA model with trust region technique is obtained and the local convergence is proved in Chapter four, and a new trust region method is proposed for solving nonlinear programming problems. At last in Chapter five the global convergence of this method is proved. In addition, some numerical tests are given, which shows that this method is efficient.更多还原