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1.
We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we develop a risk-averse policy iteration method and we prove its convergence. We also propose a version of the Newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence. Finally, we discuss relations to min–max Markov decision models.  相似文献   

2.
In this paper we present some non-interior path-following methods for linear complementarity problems. Instead of using the standard central path we use a scaled central path. Based on this new central path, we first give a feasible non-interior path-following method for linear complementarity problems. And then we extend it to an infeasible method. After proving the boundedness of the neighborhood, we prove the convergence of our method. Another point we should present is that we prove the local quadratic convergence of feasible method without the assumption of strict complementarity at the solution.  相似文献   

3.
For a risk-averse multistage stochastic optimization problem with a finite scenario tree, we introduce a new scenario decomposition method and we prove its convergence. The main idea of the method is to construct a family of risk-neutral approximations of the problem. The method is applied to a risk-averse inventory and assembly problem. In addition, we develop a partially regularized bundle method for nonsmooth optimization.  相似文献   

4.
系统动力学模型结构分析中表函数的改进方法   总被引:4,自引:0,他引:4  
分析了非线性系统动力学(SD)模型中表函数环节的传统表示方法,指出该方法对于进行SD模型的结构分析所造成的障碍,并提出了用牛顿插值的承袭性算法来改进表函数环节的表示方法的思路.接着分别介绍了用差商和差分牛顿插值法改进表函数的过程.最后,通过一个实例说明了表函数改进的方法,并展示了以此为基础进行结构分析的思路.  相似文献   

5.
In this paper, we suggest a convergent numerical method for solving nonlinear delay Volterra integro-differential equations. First, we convert the problem into a continuous-time optimization problem and then use a shifted pseudospectral method to discrete the problem. Having solved the last problem, we can achieve the pointwise and continuous approximate solutions for the main delay Volterra integro-differential equations. Here, we analyze the convergence of the method and solve some numerical examples to show the efficiency of the method.  相似文献   

6.
张卷美 《大学数学》2007,23(6):135-139
迭代方法是求解非线性方程近似根的重要方法.本文基于隐函数存在定理,提出了一种新的迭代方法收敛性和收敛阶数的证明方法,并分别对牛顿(Newton)和柯西(Cauchy)迭代方法迭代收敛性和收敛阶数进行了证明.最后,利用本文提出的证明方法,证明了基于三次泰勒(Taylor)展式构成的迭代格式是收敛的,收敛阶数至少为4,并提出猜想,基于n次泰勒展式构成的迭代格式是收敛的,收敛阶数至少为(n+1).  相似文献   

7.
In this paper, we propose a parallel exact method to solve bi-objective combinatorial optimization problems. This method has been inspired by the two-phase method which is a very general scheme to optimally solve bi-objective combinatorial optimization problems. Here, we first show that applying such a method to a particular problem allows improvements. Secondly, we propose a parallel model to speed up the search. Experiments have been carried out on a bi-objective permutation flowshop problem for which we also propose a new lower bound.  相似文献   

8.
系统聚类分析中应注意的两类问题   总被引:2,自引:0,他引:2  
给出了选用九种相似性度量,用最短距离法聚类,结果互不相同的一个有趣的例子。对该例,用欧氏距离求出距离矩阵后,除用最短距离法聚类结果唯一外,用最长距离法、重心法、类平均法、离差平方和法聚类,结果均不唯一。  相似文献   

9.
In this paper, we propose a quasi-Newton method for solving systems of monotone equations. The method is a combination of the Broyden method and the hyperplane projection method. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method is promising.  相似文献   

10.
Quasi-Newton method is a well-known effective method for solving optimization problems. Since it is a line search method, which needs a line search procedure after determining a search direction at each iteration, we must decide a line search rule to choose a step size along a search direction. In this paper, we propose a new inexact line search rule for quasi-Newton method and establish some global convergent results of this method. These results are useful in designing new quasi-Newton methods. Moreover, we analyze the convergence rate of quasi-Newton method with the new line search rule.  相似文献   

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