Both theoretical proof and numerical experiments indicate that this algorithm is convergent and effective for solving large-scale semidefinite programming . in the following section, we work over the bisection problems 数值实验与理论分析均表明该算法适用于求解大规模问题,且具有良好的收敛性;其次,研究了电路二等分问题。
A strength relaxation of semidefinite programming for standard quadratic optimization problems is given . the relaxation is transformed to a semi-indefinite programming . a linear programming cutting plane algorithm is proposed 3.给出标准二次优化问题的一个强化半定规划松弛模型,把该模型转化为半不定的线性规划问题,并提出线性规划的一种新的割平面算法解该问题,理论和数值实验证明了算法的有效性
In recent years, the theory and algorithm for semidefinite programming have developed greatly, and its most important applications are found in combinatorial optimization, system engineering and electrical engineering . semidefinite programming is a new and important research field in mathematical programming 近年来其理论和算法取得了很大的进展,并且在组合优化、系统工程和电子工程等领域得到广泛的应用,已经成为数学规划领域中一个新的活跃的研究方向
In recent years, the theory and algorithm for semidefinite programming have developed greatly, and its most important applications are found in combinatorial optimization, system engineering and electrical engineering . semidefinite programming is a new and important research field in mathematical programming 近年来其理论和算法取得了很大的进展,并且在组合优化、系统工程和电子工程等领域得到广泛的应用,已经成为数学规划领域中一个新的活跃的研究方向
An equivalent integral programming model and a new semidefinite programming relaxation for the max-bisection problem are given . then, we solve the relaxation with a projected gradient algorithm . coupled with the randomized method, an approximate solution of the max-bisection problem is obtained 2.给出图的最大二等分问题的整数规划模型的等价模型及其新的半定规划松弛模型,利用投影梯度算法求解该半定规划松弛模型,然后利用随机扰动算法求得原问题的次优解
Furthermore, an approach of one destination to another is studied and a mathematical model and corresponding algorithm to solve the problem of qos routing is given, in which semidefinite programming is used . the basic problem of qos routing is an optimal problem satisfying multi-constrained conditions from a source node to one destination 此外,本论文还研究了点到点的多路路由选择问题,并给出了一种求解qos路由问题的数学模型及算法,用半定规划的方法进行了求解。
In recent years, the theory and algorithm for semidefinite programming have developed greatly, and it's most important applications are found in system theory, control theory, combinatorial optimization and mobile cotmnunication . semidefinite programming is a new and important research field in mathematical programming 近年来其理论和算法取得了很大的进展,并且在系统论、控制论、组合优化和移动通信等领域中获得广泛的应用,成为数学规划领域中一个新的活跃的研究方向
In recent years, the theory and algorithm for semidefinite programming have developed greatly, and it's most important applications are found in system theory, control theory, combinatorial optimization and mobile cotmnunication . semidefinite programming is a new and important research field in mathematical programming 近年来其理论和算法取得了很大的进展,并且在系统论、控制论、组合优化和移动通信等领域中获得广泛的应用,成为数学规划领域中一个新的活跃的研究方向
In the paper, we firstly summarize the theory, algorithm, application and recent research of semidefinite programming, then, introduce our some work in algorithm and application . for detail, we conclude them as follows : 1 . a nonlinear programming algorithm was proposed for the max-bisection problem, and the convergent result was given 本文首先介绍了半定规划的基本知识,包括半定规划的理论、算法、应用和研究现状,然后在半定规划的算法和应用方面做了一些工作,具体如下:1.对图的最大二等分问题提出一种非线性规划算法,并给出该算法的收敛性证明
It is significantly important to discuss semidefmite programming . its most important applications are found within many fields; on the other hand, several classical optimization problems can be formulated as standard semidefinite programming . therefore semidefinite programming provides a unit form to study these problems and construct algorithms 半定规划为研究这一系列凸规划问题并构造算法提供了统一的数学框架,而且半定规划在控制理论、信号处理、特征值优化和组合优化等领域已获得成功的应用,因此半定规划在近几年备受关注。