随机规划中的一些逼近结果

主要讨论了一类随机规划的目标函数分别在概率测度序列分布收敛、函数序列上图收敛以及随机变量序列均方可积收敛等收敛意义下目标函数序列的收敛情况。基于上述收敛情况给出了一些逼近思想，这些思想可应用于求解这类随机规划问题。     

随机规划的弱微分性

本文将随机函数ｖ（ｘ，ω）引入随机规划问题ｚ（ｖ（ω）＝ｓｕｐｙ∈Ｙ｛Ｅｆ（ｖ（ω），ｙ）│Ｅｇｉ（Ｖ（ω），ｙ）≤０，ｊ＝１，Ｊ｝中。对相应的最优化问题的稳定性和最优值函数的可微性作了一些探讨。     

一种解带补偿的随机规划的逼近方法

其中f(x)∈C~1且f(x)为凸函数,A∈IR~(m×n),x∈IR~n,b∈IR~m.(1)的一般形式可用可行方向法(Topkis-Veinott情形)得到一个Fritz-John点.但当f(x)或△f(x)太复杂以致难以计算时,此方法就不适当.为此考虑逼近问题:     

解线性约束凸规划的次最优化方法和改进

1.引 言 关于线性约束下的非线性规划,很多人进行了研究,Zangwill[3] 于1967年提出了次最优化方法,该方法的原理是将原规划问题化为一系列只含有等式约束的子问题求解,最后找到最优解所在的流形,在此流形上使用无约束规划的各种方法求解原问题即可.薛声家[2]1983     

补偿随机规划的一种新数值方法

本文给出解决两阶段求援随机规划的一种新的数值方法.由于引进了新的逼近技术,该方法具有全局收敛性和局部超线性收敛性.     

补偿随机规划的一种新数值方法

本文给出解决两阶段求援随机规划的一种新的数值方法.由于引进了新的逼近技术,该方法具有全局收敛性和局部超线性收敛性。     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

解带有二次约束二次规划的一个整体优化方法

在本文中，我们提出了一种解带有二次约束二次规划问题（QP）的新算法，这种方法是基于单纯形分枝定界技术，其中包括极小极大问题和线性规划问题作为子问题，利用拉格朗日松弛和投影次梯度方法来确定问题（QP）最优值的下界，在问题（QP）的可行域是n维的条件下，如果这个算法有限步后终止，得到的点必是问题（QP）的整体最优解；否则，该算法产生的点的序列{v^k}的每一个聚点也必是问题（QP）的整体最优解。     

二层随机规划基于随机模拟的遗传算法

本提出了二层随机规划模型，给出了求解二层随机规划问题的基于随机模拟的遗传算法。实际算例表明算法是可行的、有效的。     

A parallel inexact newton method for stochastic programs with recourse

A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear convergence of the method are established. Furthermore, the method provides an error estimate which does not require much extra computation. The performance of the method is illustrated on a CM5 parallel computer.This work was supported by the Australian Research Council and the numerical experiments were done on the Sydney Regional Centre for Parallel Computing CM5.     

Continuity of parametric mixed-integer quadratic programs and its application to stability analysis of two-stage quadratic stochastic programs with mixed-integer recourse

For mixed-integer quadratic program where all coefficients in the objective function and the right-hand sides of constraints vary simultaneously, we show locally Lipschitz continuity of its optimal value function, and derive the corresponding global estimation; furthermore, we also obtain quantitative estimation about the change of its optimal solutions. Applying these results to two-stage quadratic stochastic program with mixed-integer recourse, we establish quantitative stability of the optimal value function and the optimal solution set with respect to the Fortet-Mourier probability metric, when the underlying probability distribution is perturbed. The obtained results generalize available results on continuity properties of mixed-integer quadratic programs and extend current results on quantitative stability of two-stage quadratic stochastic programs with mixed-integer recourse.     

一类带有MaxEMin评判的补偿型随机规划算法

补偿型随机规划一般假定随机变量的概率分布具有完备信息, 但实际情况往往只能获得部分信息. 针对离散概率具有一类线性部分信息条件而建立了带有MaxEMin评判的两阶段随机规划模型, 借助二次规划和对偶分解方法得到了可行性切割和最优切割, 给出了基于L-型的求解算法, 并证明了算法的收敛性. 通过数值实验表明了算法的有效性.     

The lagrange-newton method for infinite-dimensional optimization problems

This paper investigates local convergence properties of the Lagrange-Newton method for optimization problems in reflexive Banach spaces. Sufficient conditions for quadratic convergence of optimal solutions and Lagrange multipliers are given. The results are applied to optimal control problems.     

Approximate nonlinear programming algorithms for solving stochastic programs with recourse

This paper summarizes the main results on approximate nonlinear programming algorithms investigated by the author. These algorithms are obtained by combining approximation and nonlinear programming algorithms. They are designed for programs in which the evaluation of the objective functions is very difficult so that only their approximate values can be obtained. Therefore, these algorithms are particularly suitable for stochastic programming problems with recourse.Project supported by the National Natural Science Foundation of China.     

A simulation-based approach to two-stage stochastic programming with recourse

In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brasília, Brazil, through a Doctoral Fellowship under grant 200595/93-8.     

Dual support method for solving convex quadratic programs

In this article, we present a new dual method for solving convex (but not strictly convex) quadratic programs (QPs). Our method is the generalization of the dual support method, developed by Gabasov and co-workers in 1981, for solving convex QPs. It proceeds in two phases: the first is to construct the initial support, called coordinator support, for the problem and the second is to achieve the optimality of the problem. Results of numerical experiments are given comparing our approach with the active-set method.     

An interior point method for quadratic programs based on conjugate projected gradients

We propose an interior point method for large-scale convex quadratic programming where no assumptions are made about the sparsity structure of the quadratic coefficient matrixQ. The interior point method we describe is a doubly iterative algorithm that invokes aconjugate projected gradient procedure to obtain the search direction. The effect is thatQ appears in a conjugate direction routine rather than in a matrix factorization. By doing this, the matrices to be factored have the same nonzero structure as those in linear programming. Further, one variant of this method istheoretically convergent with onlyone matrix factorization throughout the procedure.     

Statistical approximations for recourse constrained stochastic programs

The two stage stochastic program with recourse is known to have numerous applications in financial planning, energy modeling, telecommunications systems etc. Notwithstanding its applicability, the two stage stochastic program is limited in its ability to incorporate a decision maker's attitudes towards risk. In this paper we present an extension via the inclusion of a recourse constraint. This results in a convex integrated chance constraint (ICC), which inherits the convexity properties of two stage programs. However, it also inherits some of the difficulties associated with the evaluation of recourse functions. This motivates our study of conditions that may be applicable to algorithms using statistical approximations of such ICC. We present a set of sufficient conditions that these approximations may satisfy in order to assure convergence. Our conditions are satisfied by a wide range of statistical approximations, and we demonstrate that these approximations can be generated within standard algorithmic procedures.This work was supported in part by Grant No. NSF-DDM-9114352 from the National Science Foundation.     

Sublinear upper bounds for stochastic programs with recourse

Separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program. The resulting problem's objective involves the inf-convolution of convex functions. A dual of this problem is formulated to obtain an implementable procedure to calculate the bound. Function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables. The sublinear bound can often be used when other suggested upper bounds are intractable. Computational results indicate that the sublinear approximation provides good, efficient bounds on the stochastic program objective value.This research has been partially supported by the National Science Foundation. The first author's work was also supported in part by Office of Naval Research Grant N00014-86-K-0628 and by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.