非线性动力系统多阶段辨识模型、算法及应用

本文针对一类发酵过程中的发育期、生长期及稳定期的不同特性，提出一种非线性多阶段动力系统及其辨识模型。论述了该模型是一种特殊的多阶段最优控制问题。根据子控制问题性能指标下水平集的局部一致有界性及下半连续性，证明了子控制问题可控性及最优解集为非空紧集。依此性质构造优化算法，研制相应的数学软件，并应用于间歇发酵过程中的参数辨识。其数值结果表明：该多阶段模型比已有模型更能逼近实际过程，提高了模型的精度，使模型更为有效。     

修正的整数DEA模型及其在中西部高校社科研究中的应用

传统的DEA模型有时并不能给出含有整数值决策单元的准确投影方向,而现有的整数DEA模型还存在投影值不准确以及模型过于复杂等不足.因此,首先指出并说明已有整数DEA模型存在的问题.其次,给出了一个修正的整数DEA模型,并讨论了模型的性质以及与已有模型的关系.考虑到现实评价中投入产出指标同时含有整数与非整数的情况,进而给出了在修正模型下的混合整数DEA模型.最后,应用提出的模型分析并比较了中国中西部102所高校的社科研究效率及优化问题.     

模糊综合评价中的若干问题

本文对当前广泛应用的模糊综合评价方法，讨论了评价因素间的补偿作用及评定级别关于权变化的稳定性问题，建立了补偿量及保级区间的定义，并证明了它们的若干性质及计算方法。从而丰富了评价信息，为全面认识参评样品的质量状态，提供了重要的辅助信息。     

有随机投资回报的随机保费模型的渐近破产概率(英文)

本文研究了随机投资回报环境下扰动的随机保费模型的破产问题.利用鞅方法和随机分析的理论讨论了盈余过程的一些基本性质,得到了一个可以用来求解破产时刻的Laplace变换的积分微分方程,结果推广了已有的随机投资问报风险模型的结论.     

δ冲击模型中截尾数据的统计推断

本文研究了δ-冲击模型中参数δ的统计推断问题，该模型具有参数为λ的Poisson冲击，系统在当两个连续的冲击时间间隔小于δ时失效，失效的时间记为T．首先，我们给出了在δ小于平均冲击间隔时间(即1／λ)的情况下，失效时间T的密度函数的性质；然后我们给出了截尾数据的损失信息补偿的方法；借助Class-K方法，给出了δ的无偏、一致估计以和区间估计．最后，由Edgeworth展开和Boostrap方法，我们得到了δ的精确度更高的区间估计．     

双重时序模型矩估计的渐近性：1.样本自协方差（自相关）函数

双重时序模型自提出以来，特别是关于模型的概率性质（如平很快稳性，遍历性）已有许多讨论，但统计推断方面的文章还很少。作为［９，１０］工作的继续，本文及后续文章将讨论矩估计及其大样本性质。首先在本文中，基本的矩估计量（样本自协方差函数及样本自相关函数）的渐近性质对ＡＲ（１）－ＭＡ（ｑ）模型得到讨论，证明了其渐近正态，并 强相合的收敛速度。     

关于矩阵奇异值p-范数的讨论的注记

指出近期矩阵奇异值p-范数的讨论中一些值得商榷的问题．应用已有的半正定Hermitian矩阵特征值和迹的性质，我们研究了相关问题．     

随机种群模型数值解的均方散逸性

讨论了随机种群模型数值解的均方散逸性,基于步长受限制和无限制的两种条件,利用补偿的和无补偿的数值方法研究了随机种群模型数值解的均方散逸性.从而得出补偿的数值算法更适合解决随机种群模型数值解的均方散逸性问题.     

广义特征值极小扰动问题的一类黎曼共轭梯度法

研究含参数$l$非方矩阵对广义特征值极小扰动问题所导出的一类复乘积流形约束矩阵最小二乘问题.与已有工作不同,本文直接针对复问题模型,结合复乘积流形的几何性质和欧式空间上的改进Fletcher-Reeves共轭梯度法,设计一类适用于问题模型的黎曼非线性共轭梯度求解算法,并给出全局收敛性分析.数值实验和数值比较表明该算法比参数$l=1$的已有算法收敛速度更快,与参数$l=n$的已有算法能得到相同精度的解.与部分其它流形优化相比与已有的黎曼Dai非线性共轭梯度法具有相当的迭代效率,与黎曼二阶算法相比单步迭代成本较低、总体迭代时间较少,与部分非流形优化算法相比在迭代效率上有明显优势.     

基于非自愿移民不同风险感知能力的多元补偿决策研究

非自愿移民在获得移民补偿后仍面临着贫困及生活不稳定等问题,这种问题产生的原因是补偿不合理,提供了一种新的移民补偿思路,那就是根据移民的风险感知能力构建多目标规划模型,并运用模拟数据验证,经检验模型能够用于为移民提供一种多元补偿组合方案,使移民能够获得未来的财产收入,是一种长效的补偿思路.     

Stochastic programming with simple integer recourse

Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic continuous programs.Analytical as well as computational properties of the expected recourse function of simple integer recourse problems are studied. This includes sharp bounds on this function and the study of the convex hull. Finally, a finite termination algorithm is obtained that solves two classes of stochastic simple integer recourse problems.Supported by the National Operations Research Network in the Netherlands (LNMB).     

Stochastic Survivable Network Design Problems

In this paper we introduce survivable network design problems under a two-stage stochastic model with fixed recourse and finitely many scenarios. We propose a new cut-based formulation based on orientation properties which is stronger than the undirected cut-based model. We use a two-stage branch&cut algorithm for solving the decomposed model to provable optimality. In order to accelerate the computations, we suggest a new cut strengthening technique for the decomposed L-shaped optimality cuts that is computationally fast and easy to implement.     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

Implementing bounds-based approximations in convex-concave two-stage stochastic programming

This paper is concerned with implementational issues and computational testing of bounds-based approximations for solving two-stage stochastic programs with fixed recourse. The implemented bounds are those derived by the authors previously, using first and cross moment information of the random parameters and a convex-concave saddle property of the recourse function. The paper first examines these bounds with regard to their tightness, monotonic behavior, convergence properties, and computationally exploitable decomposition structures. Subsequently, the bounds are implemented under various partitioning/refining strategies for the successive approximation. The detailed numerical experiments demonstrate the effectiveness in solving large scenario-based two-stage stochastic optimization problems throughsuccessive scenario clusters induced by refining the approximations.     

Distribution functions in stochastic programs with recourse: A parametric analysis

This paper studies the behavior of the optimum value of a two-stage stochastic program with recourse (random right-hand sides) as the mean and covariance matrices defining the random variables in the program are perturbed. Several results for convex programs are developed and are used to study the effect such perturbations have on the regularity properties of the stochastic programs. Cost associated with incorrectly specifying the mean and covariance matrices are discussed and estimated. A stochastic programming model in which the random variable is dependent on the first-stage decision is presented.     

Quantitative stability of full random two-stage stochastic programs with recourse

In this paper, we consider quantitative stability analysis for two-stage stochastic linear programs when recourse costs, the technology matrix, the recourse matrix and the right-hand side vector are all random. For this purpose, we first investigate continuity properties of parametric linear programs. After deriving an explicit expression for the upper bound of its feasible solutions, we establish locally Lipschitz continuity of the feasible solution sets of parametric linear programs. These results are then applied to prove continuity of the generalized objective function derived from the full random second-stage recourse problem, from which we derive new forms of quantitative stability results of the optimal value function and the optimal solution set with respect to the Fortet–Mourier probability metric. The obtained results are finally applied to establish asymptotic behavior of an empirical approximation algorithm for full random two-stage stochastic programs.     

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.     

A simple recourse model for power dispatch under uncertain demand

Optimal power dispatch under uncertainty of power demand is tackled via a stochastic programming model with simple recourse. The decision variables correspond to generation policies of a system comprising thermal units, pumped storage plants and energy contracts. The paper is a case study to test the kernel estimation method in the context of stochastic programming. Kernel estimates are used to approximate the unknown probability distribution of power demand. General stability results from stochastic programming yield the asymptotic stability of optimal solutions. Kernel estimates lead to favourable numerical properties of the recourse model (no numerical integration, the optimization problem is smooth convex and of moderate dimension). Test runs based on real-life data are reported. We compute the value of the stochastic solution for different problem instances and compare the stochastic programming solution with deterministic solutions involving adjusted demand portions.This research is supported by the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung of the Deutsche Forschungsgemeinschaft.     

Multi-period stochastic portfolio optimization: Block-separable decomposition

We consider a multiperiod stochastic programming recourse model for stock portfolio optimization. The presence of various risk and policy constraints leads to significant period-by-period linkage in the model. Furthermore, the dimensionality of the model is large due to many securities under consideration. We propose exploiting block separable recourse structure as well as methods of inducing such structure within nested L-shaped decomposition. We test the model and solution methodology with a base consisting of the Standard & Poor 100 stocks and experiment with several variants of the block separable technique. These are then compared to the standard nested period-by-period decomposition algorithm. It turns out that for financial optimization models of the kind that are discussed in this paper, significant computational efficiencies can be gained with the proposed methodology.     

一般形式多阶段有补偿问题的广义对偶理论

本文在文［１］的基础上，讨论一般形式多阶段有补偿非线性随机规划问题的广义对偶理论与最优化性条件．通过发掘凸规划对偶理论的本质，首先推广了与通常规划问题对偶理论有关的概念的含义，由此构造出所论问题在等价意义下的广义原始泛函与广义对偶泛函，进而得到其广义对偶理论，所得结论不仅能恰当合理地反映问题本身的属性，而且有关定理的表述形式简明、结论较强，可直接应用于多阶段有补偿问题的其它理论研究与数值求解算法的设计中去．上述结果与所用研究方法均推广和发展了通常的对偶理论