Asymptotic synchronization of continuous/discrete complex dynamical networks by optimal partitioning method

The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015     

Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

针对限制幅值磁共振脉冲的优化设计

在磁共振脉冲优化领域,优化脉冲普遍存在幅值过大的问题,这极大地限制了优化脉冲的使用范围。为了限制优化脉冲的幅值,扩大其应用范围,提出了一种基于L-BFGS-B数值算法的脉冲优化设计方法。首先基于Liouville-von Neuman方程,使用最优控制思想构建优化模型;然后使用L-BFGS-B算法,在限制幅值的条件下对优化模型进行数值迭代求解;最后以脉冲的激发效率以及激发轮廓的均匀性作为衡量优化脉冲优劣的标准对该方法进行仿真和实验验证。结果表明,采用该方法获得的优化脉冲在幅值被限制的前提下,仍能获得较传统磁共振脉冲更好的共振激发效果,进而增强信号的灵敏度,提高图像的质量。     

基于背景最佳滤波尺度的红外图像复杂度评价准则

提出一种基于背景最佳滤波尺度的红外图像复杂度评价准则来解决传统方法评价背景效果较差的问题. 同时, 这种方法还可以为红外图像滤波提供最佳高通滤波尺度信息, 从而对红外图像进行性能最佳滤波. 首先, 生成高斯仿真目标并与红外图像进行融合, 获得包含仿真目标及真实红外背景的图像. 然后, 在不同高斯滤波尺度下对图像滤波, 并计算滤波后仿真目标的信噪比. 最后, 取滤波后目标信噪比最大时的滤波尺度作为背景最佳滤波尺度, 使用该尺度可评价红外图像的复杂度. 另外, 本文还使用数学模型推导了红外图像最佳滤波尺度, 得出最佳滤波尺度的数学表达式. 大量实验表明: 1) 本文推导的最佳滤波尺度数学表达式与实验曲线吻合. 2) 这种方法在评价红外图像复杂度方面比传统的基于信息熵的方法效果要好很多. 并且这种方法获取的红外背景复杂度为滤波最佳尺度, 可以直接利用这项指标对图像进行最佳滤波从而更好地检测弱小目标. 3) 仿真目标尺度越大, 最佳滤波尺度也会相应增大. 因此, 在评价图像复杂度时, 应使用相同尺度的仿真目标, 不同图像之间才具备可比性. 同时, 最佳滤波尺度与仿真目标的强度无关. 4) 本文算法使用的滤波器宜用高斯及Butterworth高通滤波器实现. 5) 本文提出的方法不仅可以有效分析红外视频的复杂度, 并且可以通过复杂度的变化分析图像内容的突变.     

Discounted dynamic programming with unbounded returns: Application to economic models

In this paper, we study discounted Markov decision processes on an uncountable state space. We allow a utility (reward) function to be unbounded both from above and below. A new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function. This assumption, in turn, enables us to prove the convergence of a value iteration algorithm to a solution to the Bellman equation. Moreover, by virtue of the optimality equation we show the existence of an optimal stationary policy.     

Parametric aggregation in ordered weighted averaging

Incorporating further information into the ordered weighted averaging (OWA) operator weights is investigated in this paper. We first prove that for a constant orness the minimax disparity model [13] has unique optimal solution while the modified minimax disparity model [16] has alternative optimal OWA weights. Multiple optimal solutions in modified minimax disparity model provide us opportunity to define a parametric aggregation OWA which gives flexibility to decision makers in the process of aggregation and selecting the best alternative. Finally, the usefulness of the proposed parametric aggregation method is illustrated with an application in metasearch engine.     

会议选址问题的优化模型

国内某公司在各省会城市都设有分支机构,公司每年都有频繁的会议和培训工作需要各地分支机构派人参加,如何在大陆地区31个省会城市里选择一个城市作为会议地址,使得举办会议的成本最低且中转次数最少.建立了该会议选址问题的双目标优化模型,收集处理了有关实际数据,利用网络最短路算法和约束法等得到了该会议选址问题的解.在不考虑中转费用的情况下,得出成本最低且中转次数最少的会议地址是西安;在考虑中转费用的情况下,根据中转费用的不同给出了可供实际决策的最优会议选址方案.     

半线性Sobolev方程的H~1-Galerkin混合有限元方法

利用H~1-Galerkin混合有限元方法研究了一维半线性Sobolev方程,得到了半离散解的最优阶误差估计,优点是不需验证LBB相容性条件.