Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and finite-time stabilization boundedness of fractional-order switched nonlinear systems with exogenous inputs. By constructing a simple Lyapunov-like function and using some properties of Caputo derivative, the authors obtain some new sufficient conditions for the problem via linear matrix inequalities, which can be efficiently solved by using existing convex algorithms. A constructive geometric is used to design switching laws amongst the subsystems. The obtained results are more general and useful than some existing works, and cover them as special cases, in which only linear fractional-order systems were presented. Numerical examples are provided to demonstrate the effectiveness of the proposed results.     

基于并行的快速碰撞检测算法

提出了一中基于并行的快速碰测算法。该算法面向动态复杂场景采用层次的自适应空间剖分方法建构物体的平衡包围盒树,然后通过并行遍历包围盒树来加速碰撞检测,算法属于ＭＤＭＤ同步并行算法,采用多线程技术实现,在单处理机和处理机上均能运行。     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters

This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the (nonsmooth) objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint, which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization, the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors’ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.     

A note on the nestedness property for ordered median problems in tree networks

The nestedness property has become an increasingly important means for devising efficient algorithms for network location problems. There have been attempts to explore the nestedness property of network location problems with some special cases of the convex ordered median objectives. However, there is little research on the nestedness property for those problems with the concave ordered median objectives. This paper constructs a tree network T and shows that the nestedness property cannot hold for the concave ordered median problem, which fills a gap in the research on the nestedness property. Finally, the authors pose an open problem on identifying the nestedness property for the continuous strategic ordered median problem.     

Convergence of Distributed Gradient-Tracking-Based Optimization Algorithms with Random Graphs

This paper studies distributed convex optimization over a multi-agent system, where each agent owns only a local cost function with convexity and Lipschitz continuous gradients. The goal of the agents is to cooperatively minimize a sum of the local cost functions. The underlying communication networks are modelled by a sequence of random and balanced digraphs, which are not required to be spatially or temporally independent and have any special distributions. The authors use a distributed gradient-tracking-based optimization algorithm to solve the optimization problem. In the algorithm,each agent makes an estimate of the optimal solution and an estimate of the average of all the local gradients. The values of the estimates are updated based on a combination of a consensus method and a gradient tracking method. The authors prove that the algorithm can achieve convergence to the optimal solution at a geometric rate if the conditional graphs are uniformly strongly connected, the global cost function is strongly convex and the step-sizes don't exceed some upper bounds.     

CONVERGENCE PROPERTIES OF PROJECTED GRADIENT METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR CONVEX CONSTRAINED OPTIMIZATION

1. IntroductionGiven some function f(x): Wu - FI over a nonempty closed set n C W", one is interestedin solving the fOllowing optimization problem with constraints amin f(x)s.t. x E n (1.1)where f(x): Q C Wu - FI is twice continuously differentiable. This problem has receivedconsiderable attention extensively. The linear constrained case where n is a polyhedron is ofspecial inferest. Recently, there are quite a few articles proposing projected gradient methodsto solve the problem (see, fo…     

求解可分离连续凸二次背包问题的直接算法

经典算法一般采用迭代过程求解连续凸二次背包问题,研究了求解可分离连续凸二次背包问题的直接算法。分析了可分离连续凸二次背包问题的结构特性,通过两个命题和两个定理研究了可分离连续凸二次背包问题的解的特性,提出了一种快速的求解该问题的直接算法。该算法能快速有效地求解可分离连续凸二次背包问题的最优解,算法的时间复杂度和空间复杂度都是O(n),都比经典算法节约很多。     

An Asset Allocation Model and Its Solving Method

Asset allocation is an important issue in finance, and both risk and return are its fundamental ingredients. Rather than the return, the measure of the risk is complicated and of controversy.In this paper, we propose an appropriate risk measure which is precisely a convex combination of mean semi-deviation and conditional value-at-risk. Based on this risk measure, investors can trade-off flexibly between the volatility and the loss to tackle the incurring risk by choosing different convex coefficients.As the presented risk measure contains nonsmooth term, the asset allocation model based on it is nonsmooth. To employ traditional gradient algorithms, we develop a uniform smooth approximation of the plus function and convert the model into a smooth one. Finally, an illustrative empirical study is given. The results indicate that investors can control risk efficiently by adjusting the convex coefficient and the confidence level simultaneously according to their perceptions. Moreover, the effectiveness of the smoothing function proposed in the paper is verified.     

常微分方程初值问题并行算法研究现状

本文对常微分方程初值问题数值求解的并行算法进行综述,给出并行算法的应用前景和构造的一些途径,同时指出并行化的主要困难和一些解决的方法。     

Scheduling problems with rejection to minimize the maximum flow time

This paper considers the scheduling problem with rejection on m identical parallel machines to minimize the maximum flow time. The authors show that this problem is NP-hard even when there is a single machine and all jobs have two distinct release dates. Furthermore, the authors present a dynamic programming algorithm and two approximation algorithms to solve them.     

A multi-period pricing and inventory control model

<正> The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each other and their distributions depend on the product price.Pricing andordering decisions are made at the beginning of each period and all shortage are backlogged.Orderingcost is a convex function of the amount ordered.The objective is to find an inventory and pricing policymaximizing expected discounted profit over the finite horizon.The authors characterize the structure ofthe optimal combined pricing and inventory strategy for this model.Moreover,the authors demonstratehow the profit-to-go function,order up to level,reorder point and optimal price change with respectto state and time.     

Resultant elimination via implicit equation interpolation

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.     

数值求解常微分方程初值问题的一类并行算法

本文给出了一类数值求解常数微分方程初值问题的并行算法，该类并行算法适用于ＭＩＭＤ型多处理机系统，具有良好的收敛性和数值稳定性，此类并行算法对Ｍｉｒａｎｋｅｒ和Ｌｉｎｉｇｅｒ１９６７年提出的一种构造思想做了圆满的解闷。     

A NEW SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE DFP ALGORITHM WITH WOLFE LINE SEARCH

ＡＮＥＷＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＴＨＥＤＦＰＡＬＧＯＲＩＴＨＭＷＩＴＨＷＯＬＦＥＬＩＮＥＳＥＡＲＣＨ￥ＸＵＤａｃｈｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖ...     

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.     

实时仿真算法的研究进展

从六个方面综述动力学系统实时仿真算法的一些最近的研究进展。讨论包括：快速实时仿真算法研究,实时组合算法与网络计算机上的实时并行算法;微分代数系统的实时算法与实时并行算法;实时间断处理;仿真模型信息传输误差估计;动力学系统仿真假解研究等一些新的思想和方法。     

Algorithm Implementation for Distributed Convex Intersection Computation

Intersection computation of convex sets is a typical problem in distributed optimization. In this paper, the algorithm implementation is investigated for distributed convex intersection computation problems. In a multi-agent network, each agent is associated with a convex set. The objective is for all the agents to achieve an agreement within the intersection of the associated convex sets. A distributed"projected consensus algorithm" is employed, and the computation of the projection term is converted to a constrained optimization problem. The solution of the optimization problem is determined by Karush-Kuhn-Tucker(KKT) conditions. Some implementable algorithms based on the simplex method are introduced to solve the optimization problem. Two numerical examples are given to illustrate the effectiveness of the algorithms.     

动力学系统数值仿真并行算法的发展

本文主要综述动力学系统仿真的非刚性、刚性系统和微分代数系统并行数值方法的一些最近发展。     

Minimizing the Risk of Absolute Ruin Under a Diffusion Approximation Model with Reinsurance and Investment

This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions.The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario.Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy.The authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.