Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization

We consider stochastic discrete optimization problems where the decision variables are nonnegative integers and propose a generalized surrogate problem methodology that modifies and extends previous work in Ref. 1. Our approach is based on an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both the actual and surrogate system states. In contrast to Ref. 1, the proposed methodology applies to arbitrary constraint sets. It is shown that, under certain conditions, the solution of the original problem is recovered from the optimal surrogate state. Applications of this approach include solutions to multicommodity resource allocation problems; in these problems, exploiting the convergence speed of the method, one can overcome the obstacle posed by the presence of local optima.     

集优化问题的广义适定性与解的稳定性

本文研究了集优化问题的适定性与解的稳定性. 首次利用嵌入技术引入了集优化问题的广义适定性概念, 得到了此类适定性的一些判定准则和特征, 并给出其充分条件. 此外, 借助一类广义Gerstewitz 函数, 建立了此类适定性与一类标量优化问题广义适定性之间的等价关系. 最后, 在适当条件下研究了含参集优化问题弱有效解映射的上半连续性和下半连续性.     

运筹学中涉及多学科的一个案例

讨论了运筹学中的一个案例,在不同条件下,它涉及不同的运筹学分支以及经济学、社会学等领域。因此,教材中如能包含若干个这种例子,对引导学生多学科、全方位思考问题将是大有裨益的。     

离散余弦变换的一种推广

离散余弦变换(DCT)在数字信号、图像处理、频谱分析、数据压缩和信息隐藏等领域有着广泛的应用.推广离散余弦变换,给出一个包含三个参数的统一表达式,并证明在许多情形新变换是正交变换.最后给出一种新型离散余弦变换,并证明它是正交变换.     

Integral Equations Involving Generalized Mittag-Leffler Function

Ukrainian Mathematical Journal - We deal with the solution of the integral equation with generalized Mittag-Leffler function $$ {E}_{alpha, beta}^{upgamma, mathrm{q}}(z) $$ specifying the...     

含极大η-单调算子的广义非线性混合似变分包含组的扰动算法和稳定性

研究了一类含极大η-单调算子的广义非线性混合似变分包含组.依据不动点理论和极大η-单调算子的预解算子技巧,在Hilbert空间中提出了一种求这类变分不等式组的逼近解的扰动迭代算法,并证明了这类算法的收敛性和稳定性.所得结果是新的,并推广和统一了近期文献中的一些相关结论.     

离散系统的广义同步

讨论两个离散系统之间的广义同步．通过构造合适的非线性耦合项,导出了驱动响应系统获得广义同步的充分条件．在一个正不变的有界集上,许多混沌映射满足这些充分条件．通过3个例子,说明了充分条件的有效性．     

离散系统的广义混沌控制

针对确定性离散动力学系统的混沌控制与反控制问题,从配置Lyapunov指数出发,提出一种实现混沌控制与反控制的一般性方法.首先给出了受控系统混沌判断的特征值条件,满足该条件的系统,将产生Devaney意义下的混沌和Li-Yorke意义下的混沌.然后通过引入非对角型反馈来调整系统雅可比矩阵元素,灵活配置系统Lyapunov指数的数值和符号,从而实现离散系统的混沌控制或反控制.给出了必要的证明和仿真实例,仿真结果表明了算法的有效性.     

有关广义中心三项式系数的3个超同余式

设b,c为整数,定义广义中心三项式系数Tn(b,c)=[xn](x2+bx+c)n=「n/2」∑k=0(n2k)(2kk)bn-2kck(n∈N={0,1,…}),这里[xn]P(x)表示多项式P(x)中xn项的系数.特别地,中心Delannoy多项式Dn(x)=Tn(2x+1,x2+x)(n ∈ N),中心三项式系数...     

On a Congruence Involving Generalized Fibonomial Coefficients

Let (F_n)_n≥0 be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as

$${\left[ {\begin{array}{*{20}{c}} n \\ k \end{array}} \right]_F} = \frac{{{F_{n - k + 1}} \cdots {F_{n - 1}}{F_n}}}{{{F_1} \cdots {F_k}}}$$

. In 2013, Marques, Sellers and Trojovský proved that if p is a prime number such that p ≡ ±1 (mod 5), then p?\({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}\) for all integers a ≥ 1. In 2010, in particular, Kilic generalized the Fibonomial coefficients for

$${\left[ {\begin{array}{*{20}{c}} n \\ k \end{array}} \right]_{F,m}} = \frac{{{F_{\left( {n - k + 1} \right)m}} \cdots {F_{\left( {n - 1} \right)m}}{F_{nm}}}}{{{F_m} \cdots {F_{km}}}}$$

. In this note, we generalize Marques, Sellers and Trojovský result to prove, in particular, that if p ≡ ±1 (mod 5), then \({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_{F,m}} \equiv 1\) (mod p), for all a ≥ 0 and m ≥ 1.

     

Stability Analysis for Discrete Biological Models Using Algebraic Methods

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems. For finite dynamical systems, methods based on Gr?bner bases and triangular sets are applied to detect steady states. The feasibility of our approach is demonstrated by the analysis of stability and bifurcations of several discrete biological models using implementations of algebraic methods.     

奇异离散线性系统的开关切换控制

In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.     

CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.     

Entropic Pairs of Operations and Generalized Endomorphisms

In this paper, we define concepts of entropic pairs of operations and the generalized endomorphism for an algebra and investigate the relationships between them. We characterize entropic pairs of operations of quasigroups and show that in some cases, the presence of a generalized endomorphism is equivalent to the entropic property for an algebra.     

一个与广义二项级数有关的随机游动问题

利用广义二项级数本文给出了随机格点最终到达给定边界的概率.     

一个与广义二项级数有关的随机游动问题

In this paper,based on the method of generalized binomial series,the probability that a random lattice point touches a given boundary line is obtained.     

Stability Analysis for Discrete Linear Multipass Processes with Non-Unit Memory

A new set of stability conditions for discrete linear multipassprocesses with non-unit memory is derived and used to developcomputationally feasible stability tests. This results in asystematic procedure which tests these conditions in a particularorder, with termination if the one just tested does not hold.The use of this procedure within the area of control systemsdesign is discussed.     

离散时滞奇异摄动控制系统的稳定性分析

对含不确定性结构的奇异摄动时滞离散控制系统进行稳定性研究.通过设计一种新的Lyapunov-Krasovskii泛函,基于Lyapunov稳定性理论,在时滞依赖情形下,采取交叉项界定技术、线性矩阵分析方法并运用引理,推出在零到奇异摄动上界的整个区间范围内系统渐近稳定,给出充分性的稳定性判据.之后,再对其进行理论加深和推...