基于非合作博弈的OFDMA-WLAN系统资源分配算法研究

为满足无线局域网中基于正交频分多址技术(OFDMA-WLAN)的多用户通信需求,提出了一种基于非合作博弈的资源分配策略,利用博弈论这一有效工具对无线网络服务质量的资源分配问题进行研究,同时将用户对信道质量的不同需求转化为多用户对不同信道资源分配的非合作博弈竞争问题。此外,还将纳什均衡问题(NEP)细分为数个变分不等式子问题,通过凸优化函数对这些子问题分别求解。数值分析结果表明,所提算法在资源分配的公平性和数据传输率方面达到了更好的折中。     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

多测度Value集相似度量

针对单一测度度量Vague集相似性上的缺陷,提出了两种Vague集的多测度相似度量.给出了一种Vague集的单形体几何表示方法,亦即将Vague集的真、假隶属度和未知度表达为划分单形体同一平面的3个三角形,进而提出了适合于度量Vague集相似性的面积测度,并结合距离测度和未知度测度构造了Vague集多测度相似度量,以在空间上体现出“点-线-面”多特征相似性度量格局.实例验证了多测度相似度量的有效性和优越性.     

基于凸包求解的简单多边形方向判断新算法

Graham ScanA求解简单多边形凸包算法简洁高效,但是对于未确定方向的简单多边形,该算法需设定一个方向求解其凸包。提出一种新的算法,该算法通过利用凸包求解的Graham ScanA算法来判断简单多边形的方向。算法取得了较好的实用效果。     

Recursive algorithms for inner ellipsoidal approximation of convex polytopes

In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a finite number of steps. For their recursive nature, the proposed algorithms are better suited to treat a quite large number of constraints than standard off-line solutions, and have their natural application to problems where the set of constraints is iteratively updated, as on-line estimation problems, nonlinear convex optimization procedures and set membership identification.     

A convex parametrization of risk-adjusted stabilizing controllers

The focal point of this paper is the synthesis of controllers under risk-specifications. In recent years there has been a growing interest in the development of techniques for controller design where, instead of requiring that the performance specifications are met for every possible value of admissible uncertainty, it is required that the risk of performance violation is below a small well-defined risk level. In contrast to previous work, where the search for the controller gains is done using randomized algorithms, the results in this paper show that for a class of uncertain linear time invariant systems, the search for the “risk-adjusted” controller can be done efficiently using deterministic algorithms. More precisely, for the case when the characteristic polynomial of the closed loop system depends affinely on the uncertainty, we provide a convex parametrization of “risk-adjusted” stabilizing controllers.     

基于环链的多面体剖分快速算法研究

利用环链提出了一种对任意多面体不添加顶点的凸剖分快速方法 ,它对多面体的剖分个数接近最少 .该方法首先从多面体的棱和对角棱所构成的所有环中 ,以最小周长选取一个最好的环 ,然后利用这个环的各个边所形成的一系列面 ,对多面体进行一次剖分 .实验证明 ,这种方法可找到对多面体不添加顶点剖分的最好剖分面 ,使剖分的次数接近最少 ,具有较好的实用价值和广泛的应用前景 .     

Sorting helps for voronoi diagrams

It is well known that, using standard models of computation, Ω(n logn) time is required to build a Voronoi diagram forn point sites. This follows from the fact that a Voronoi diagram algorithm can be used to sort. However, if the sites are sorted before we start, can the Voronoi diagram be built any faster? We show that for certain interesting, although nonstandard, types of Voronoi diagrams, sorting helps. These nonstandard types of Voronoi diagrams use a convex distance function instead of the standard Euclidean distance. A convex distance function exists for any convex shape, but the distance functions based on polygons (especially triangles) lead to particularly efficient Voronoi diagram algorithms. Specifically, a Voronoi diagram using a convex distance function based on a triangle can be built inO (n log logn) time after initially sorting then sites twice. Convex distance functions based on other polygons require more initial sorting.     

R~n上的r-次微分与r-凸性

提出了Ｒｎ上的ｒ－次微分与ｒ－凸性的概念，利用ｒ－次微分，给出了许多局部极小（极大）不能满足的全局极小（极大）的一个新的必要条件，利用ｒ－凸性给出了全局极小的充分条件。ｒ－凸函数是较凸函数更大的一类凸函数，有些ｒ－凸出数是处处不连续的，且ｒ－凸函数保持凸函数一些优良特性，ｒ－凸函数的局部极小总是全局极小。