High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.

A multifractal model for linking Lagrangian and Eulerian velocity structure functions

A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.

EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.

A New Augmented Lagrangian Objective Penalty Function for Constrained Optimization Problems

In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.

Path Integral Quantization of Non-Natural Lagrangian

Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.

有约束极大极小优化问题的修正Lagrangian算法

对于有不等式约束的极大极小优化问题,本文构造了一个修正的Lagrangian函数并分析了其在一般条件下的性质,建立了与之对应的修正Lagrangian算法.最后对文献中的几个问题给出了数值计算结果验证了算法.

双曲型Lagrangian函数

双曲复数与Ｍｉｎｋｏｗｓｋｉ几何相对应，由四维时空间隔不变量和双曲型Ｌｏｒｅｎｔｚ变换可导出双曲型Ｌａｇｒａｎｇｉａｎ方程和Ｈａｍｉｌｔｏｎ＿Ｊａｃｏｂｉ方程·

多元统计分析中一类矩阵迹函数极小化问题的分裂迭代法

研究了来源于多元统计分析中的一类含列正交约束的矩阵迹函数极小化模型,该模型的特殊形式广泛应用于多维标度分析中DEDICOM模型和正交INDSCAL模型最小二乘拟合等问题中。结合变量分裂构造了几类经典的基于分裂的不可行迭代算法求解该约束迹函数极小化模型,并给出算法外层迭代框架和内层子问题的具体求解方案。数值实验验证了算法的有效性。

软件定义并行多径SFC编排

网络功能虚拟化(Network Functions Virtualization, NFV)技术可以通过动态实例化以及根据随时间变化的服务需求去动态地部署虚拟网络功能。基于NFV的多域网络切片中服务功能链(Service Function Chaining, SFC)的编排问题研究缺乏考虑多域场景,大多数启发式算法仅仅考虑了上界,SFC映射策略无法满足低时延高可靠要求。建立了面向并行业务流服务时延优化的数学模型,并进一步基于拉格朗日松弛法提出了一种考虑了下界的启发式SFC映射策略,可以有效地降低时延,提高服务的可靠性。与多租户边缘网络中可靠的SFC编排算法以及多路径低延迟SFC编排算法相比,所提算法平均包交付率分别提升了3.3%和7.4%,平均资源消耗分别降低了9%和19.2%。

SDN/NFV中基于负载均衡的服务功能链嵌入策略

针对支持网络功能虚拟化(Network Function Virtualization,NFV)的软件定义网络(SDN)中,单播请求流通常需要由多个虚拟网络功能(Virtual Network Functions,VNFs)依序组成的服务功能链(Service Function Chain,SFC)进行处理。首先联合考虑VNF动态放置,多资源及QoS约束,以最小化资源消耗成本及自动确保网络负载均衡为目标定义了动态的SFC部署问题。接着设计考虑边际成本的资源相对成本函数并利用整数线性规划对该问题建模。然后,创新地设计了一个动态辅助边权图并基于拉格朗日松弛方法构建具有自动负载均衡的服务功能链嵌入算法(SFC Embedding Algorithm,SFC-EA)对原问题求解。仿真结果表明,SFC-EA能有效解决多资源及多QoS约束下的SFC顺序嵌入这个NP难问题,并能自动确保网络负载均衡,提高网络吞吐量和流接受率。

应用Lagrangian乘子与对称罚函数结合算法分析实心轮胎动接触问题

实心轮胎动接触问题是轮胎力学领域里的新课题 ,本文提出了Lagrangian乘子与对称罚函数法的结合算法 ,并以某履带车辆实心轮胎为例 ,应用该方法对其进行了动接触的有限元力学分析 ,获得了实心轮胎稳态滚动的应力场及接触变形情况。有限元计算结果表明该算法可以有效分析实心轮胎的动接触问题 ,而且对其结构优化。

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

具有未知参数的拉格朗日系统的安全跟踪控制

针对具有未知参数的拉格朗日系统,研究了安全跟踪控制问题。首先采用backstepping方法,设计跟踪控制器用于解决系统的轨迹跟踪问题。其次构造了自适应控制障碍函数,通过该函数得到的安全控制器确保系统状态远离安全集的边界。然后结合所提出的跟踪控制器以及自适应控制障碍函数约束产生了二次规划,基于二次规划设计安全跟踪控制器,使得系统安全的同时尽可能地跟踪到参考信号。最后仿真结果验证了所提出方法的有效性。

基于不等式约束的一类新的增广Lagrangian函数

针对含不等式约束的非线性规划问题,提出了一类新的增广Lagrangian函数,证明了其稳定点、整体极小点与原约束问题KKT点、整体极小点有对应关系,增广Lagrangian函数的局部极小点为原问题的局部极小点.基于给出的新的增广Lagrangian函数进行了数值计算,验证了其可行性和有效性.

半无限规划的一个非线性 Lagrangian对偶模型(英文)

本文给出半无限规划的一个对偶罚函数模型,该模型能处理目标函数不是凸函数的情形,从而凸(SIP)对偶为该模型的一个特例.并且,作为罚函数,本模型的罚因子比l1-罚函数要小,这使得算法更可行,最后,给出零对偶间隙证明.

一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性(英文)

针对一般的非线性规划问题,利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型,并证明它与原问题之间存在零对偶间隙．针对具体的一类增广La- grangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题,详细讨论了零对偶间隙的存在性．进一步,讨论了在最优路径存在的前提下,最优路径的收敛性质．

一般约束非线性优化的增广Lagrangian算法

构造了一个求解一般约束非线性优化问题的增广Lagrangian算法 ,通过引进函数 φ(x) =max{g(x) ,- λr}可直接处理不等式的约束情形 .并且每次只需近似地求出对应增广Lagrangian罚函数的局部最小点 .在一般假设下 ,算法产生的点列的任意聚点都是问题的K

Higher-Order Lagrangian Equations of Higher-Order Motive Mechanical System

In this paper, if the condition of variation δt = 0 is satisfied, the higher-order Lagrangian equations and higher-order Hamilton＇s equations, which show the consistency with the results of traditional analytical mechanics, are obtained from the higher-order Lagrangian equations and higher-order Hamilton＇s equations. The results can enrich the theory of analytical mechanics.

The Polynomial Function Model in Born-Infeld Theory

Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation,we investigate the polynomial function model in Born-Infeld theory in this paper with the form of-([10α(φ′)^(2)]φ′)′=λf(φ(x)),whereλ>0 is a real parameter,f∈C 2(0,+∞)is a nonlinear function.We are interested in the exact number of positive solutions of the above nonlinear equation.We specifically develop for the problem combined with a careful analysis of a time-map method.