求解离散多准则决策问题的一种交互法

本文在 [1 ]的基础上发展了一种求解离散多准则决策问题的交互法 ,并举例说明其具体应用情况     

A Descriptive Approach to Multiple-Criteria Decision Making

Certain concepts from multivariate statistical analysis are applied to problems in multiple-criteria decision making. The aim of this approach is to identify basic relationships and conflicts between the available decision alternatives and between criteria. If these aspects can be clearly identified and conveyed to the responsible decision maker, he may well be in a position to make an intelligent selection of a course of action, without the need for formal utility analysis, computation of Pareto optimal sets, etc. Two appropriate multivariate statistical techniques are introduced to illustrate the approach, and each technique is applied to two sample problems.     

A Bayesian Decision Theory Approach to Classification Problems

We address the classification problem where an item is declared to be from populationπ_jif certain of its characteristicsvare assumed to be sampled from the distribution with pdf f_j(vθ_j), wherej=1, 2, …, m. We first solve the two population classification problem and then extend the results to the generalmpopulation classification problem. Usually only the form of the pdf's is known. To use the classical classification rule the parameters,θ_j, must be replaced by their estimates. In this paper we allow the parameters of the underlying distributions to be generated from prior distributions. With this added structure, we obtain Bayes rules based on predictive distributions and these are completely determined. Using the first-order expansion of the predictive density, where the coefficients of powers ofn⁻¹remain uniformly bounded innwhen integrated, we obtain an asymptotic bound for the Bayes risk.     

A Numerical Approach for Solving Some Convex Maximization Problems

We are concerned with concave programming or the convex maximization problem. In this paper, we propose a method and algorithm for solving the problem which are based on the global optimality conditions first obtained by Strekalovsky (Soviet Mathematical Doklady, 8(1987)). The method continues approaches given in (Journal of global optimization, 8(1996); Journal of Nolinear and convex Analyses 4(1)(2003)). Under certain assumptions a convergence property of the proposed method has been established. Some computational results are reported. Also, it has been shown that the problem of finding the largest eigenvalue can be found by the proposed method.     

Analysis and Solving SAT and MAX-SAT Problems Using an L-partition Approach

In this paper, we study SAT and MAX-SAT using the integer linear programming models and L-partition approach. This approach can be applied to analyze and solve many discrete optimization problems including location, covering, scheduling problems. We describe examples of SAT and MAX-SAT families for which the cardinality of L-covering of the relaxation polytope grows exponentially with the number of variables. These properties are useful in analysis and development of algorithms based on the linear relaxation of the problems. Besides we present the L-class enumeration algorithm for SAT using the L-partition approach. In addition we consider an application of this algorithm to construct exact algorithm and local search algorithms for the MAX-SAT problem.     

一种具有区间数信息的多目标指派方法

针对具有区间数信息的多目标指派问题,给出了一种指派方法。首先,将不同类型目标的区间数损益矩阵规范化为区间数成本矩阵,并应用区间数运算法则构建区间数多目标指派问题的总成本矩阵。然后,通过事先定义的任意两个区间数的序关系,将区间数指派问题优化模型转化为一个双目标优化模型,并采用线性加权法将其转化为单目标优化模型来进行求解,同时还考虑了如何处理人员数量与任务数量不相等的情形的指派问题;最后,通过一个实例分析说明了本文给出方法的可行性和有效性。本文的方法丰富了已有的求解方法,具有实际应用价值。     

求解非线性互补问题的微分方程方法

本文构造了一种求解非线性互补问题的微分方程方法.在一定条件下,证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法.在适当的条件下,证明了此算法产生的序列解是收敛的.本文最后给出了数值结果,该结果表明了此微分方程方法的有效性.     

An Approach to Solving Inverse Eigenvalue Problems for Matrices

The paper considers different formulations of inverse eigenvalue problems for matrices whose entries either polynomially or rationally depend on unknown parameters. An approach to solving inverse problems together with numerical algorithms is suggested. The solution of inverse problems is reduced to the problem of finding the so-called discrete solutions of nonlinear algebraic systems. The corresponding systems are constructed using the method of traces, and their discrete roots are found by applying the algorithms for solving nonlinear algebraic systems in several variables previously suggested by the author. Bibliography: 30 titles.     

A Gridding Method for Bayesian Sequential Decision Problems

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.     

A New Duality Approach to Solving Concave Vector Maximization Problems

We introduce a special class of monotonic functions with the help of support functions and polar sets, and use it to construct a scalarized problem and its dual for a vector optimization problem. The dual construction allows us to develop a new method for generating weak efficient solutions of a concave vector maximization problem and establish its convergence. Some numerical examples are given to illustrate the applicability of the method.     

A Vector Minimum Superharmonic Approach to Solving Infinite-Horizon Discounted Markov Decision Processes

In this paper a new algorithm is provided for obtaining approximately optimal policies for infinite-horizon discounted Markov decision processes. In addition, some of the properties of the algorithm are established. The algorithm is based upon the fact that the optimal value function is the unique vector minimum function within the superharmonic set.     

求解互补问题的一种序列二次规划方法

通过将互补问题转化为一种带非负约束的极小化问题 ,给出了求解互补问题的一种序列二次规划方法 .该方法中每一个子问题都是可解的 ,迭代产生的序列是非负的 ,在适当的条件下 ,分别证明了算法的全局收敛性、局部超线收敛性以及局部二次收敛性 .     

求解P0函数互补问题的一种微分方程方法

本针对P0函数互补问题，给出了一种微方程方法，并且证明了P0函数互补问题的解是微分方程系统的渐进稳定平衡点。在适当的假设条件下，证明了所给出的算法具有二次收敛速度。几个数值例子表明了该算法的有效性。     

Interval Approach to Solving Parametric Identification Problems for Dynamical Systems

Differential Equations - We present an approach to solving parametric identification problems for dynamical systems. The approach is aimed at finding an interval estimate of the model parameters in...     

基于粒子群算法的非线性二层规划问题的求解算法

粒子群算法（Particle Swarm Optimization，PSO）是一种新兴的优化技术，其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现，可调参数少，已得到了广泛研究和应用。本文根据该算法能够有效的求出非凸数学规划全局最优解的特点，对非线性二层规划的上下层问题求解，并根据二层规划的特点，给出了求解非线性二层规划问题全局最优解的有效算法。数值计算结果表明该算法有效。     

Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family {P_q} of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented. This work was partially supported by the Università Ca’ Foscari, Venezia, Italy, the MIUR (PRIN cofinancing 2005), the Council for Grants (under RF President) and State Aid to Fundamental Science Schools (Grant NSh-4113.2008.6). We thank Angelo Miele, Panos Pardalos and the anonymous referees for comments and suggestions.     

组合数学与数论间的一些交叉问题初探

我们证明了有限域上的一类方程组解的个数与图的顶点着色数有密切关系，而这又对许多着色问题的产生了许多应用。另外，我们也用图论的一些技巧解决了数论中一些问题。     

A $theta$-$L$ Approach for Solving Solid-State Dewetting Problems

We propose a $theta$-$L$ approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies. The sharp-interface model is governed by surface diffusion and contact line migration. For solving the model, traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble. In the $theta$-$L$ approach, we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables (i.e., the tangential angle $theta$ and the total length $L$ of the interface curve), so that it not only could reduce the stiffness resulted from the surface tension, but also could ensure the mesh equidistribution property during the evolution. Furthermore, it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method. Numerical results are reported to demonstrate that the proposed $theta$-$L$ approach is efficient and accurate.