共查询到20条相似文献,搜索用时 218 毫秒
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拟变分不等式问题是变分不等式问题的一种推广,超平面投影算法是解变分不等式的一种重要方法.通过构造严格分离当前点与拟变分不等式解集的超平面,建立了解拟变分不等式的超平面投影算法.在一定的条件下,证明了该算法的全局收敛性. 相似文献
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文章讨论了到复射影空间PN (C)的全纯曲线交超平面的问题,借助Vandermonde行列式, 构造了一些具有N+1个例外超平面的非线性退化的全纯曲线和具有2N个例外超平面的线性退化的非常映射全纯曲线,说明了 Nochka 的全纯曲线的第二基本定理是最优的.最后还构造了具有2N个例外值的N值非常数代数体函数. 相似文献
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具有限时滞一阶线性泛函微分方程的稳定性区域划分 总被引:1,自引:0,他引:1
讨论了一阶线性有限时滞泛函微分方程的稳定性区域,用一个超平面把参数空间划分为不同的稳定性区域.这个超平面上的每一点对应于特征方程在纯虚轴上至少存在一个零根(原点除外),所得结论可用于Hofp分枝分析和控制理论. 相似文献
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该文给出Banach空间X的对偶空间X~*中闭超平面上度量投影的表达式,并在Banach空间中研究了闭超平面上度量投影的连续性. 相似文献
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<正> 高维布朗运动中,超平面的首中点分布已见于[1].最近又求出了超平面的首中时分布.本文首先给出用禁止密度表示的超平面首中点与首中时之联合分布;然后由从带域内出发的布朗运动终将离开此带域着手,证明了任一布朗运动必中任一超平面,由此得出布朗运动穿越超平面(及带域)无穷多次的结论;最后研究了首达超平面(及带域)前 相似文献
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研究了多元球体上的积分中值定理的中间点的渐近性质,证明了当球体半径趋于0时,中间点近似落在过球体中心的切平面上. 相似文献
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A median hyperplane in d-dimensional space minimizes the weighted sum of the distances from a finite set of points to it. When the distances from these points are measured by possibly different gauges, we prove the existence of a median hyperplane passing through at least one of the points. When all the gauges are equal, some median hyperplane will pass through at least d-1 points, this number being increased to d when the gauge is symmetric, i.e. the gauge is a norm.Whereas some of these results have been obtained previously by different methods, we show that they all derive from a simple formula for the distance of a point to a hyperplane as measured by an arbitrary gauge. 相似文献
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This study proposes two derivative-free approaches for solving systems of large-scale nonlinear equations, where the underlying functions of the systems are continuous and satisfy a monotonicity condition. First, the framework generates a specific direction then employs a backtracking line search along this direction to construct a new point. If the new point solves the problem, the process will be stopped. Under other circumstances, the projection technique constructs an appropriate hyperplane strictly separating the current iterate from the solutions of the problem. Then the projection of the new point onto the hyperplane will determine the next iterate. Thanks to the low memory requirement of derivative-free conjugate gradient approaches, this work takes advantages of two new derivative-free conjugate gradient directions. Under appropriate conditions, the global convergence result of the recommended procedures is established. Preliminary numerical results indicate that the proposed approaches are interesting and remarkably promising. 相似文献
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Katta G. Murty 《Optimization Letters》2009,3(2):211-237
We consider the problem of developing an efficient algorithm for enumerating the extreme points of a convex polytope specified
by linear constraints. Murty and Chung (Math Program 70:27–45, 1995) introduced the concept of a segment of a polytope, and used it to develop some steps for carrying out the enumeration efficiently until the convex hull of the
set of known extreme points becomes a segment. That effort stops with a segment, other steps outlined in Murty and Chung (Math
Program 70:27–45, 1995) for carrying out the enumeration after reaching a segment, or for checking whether the segment is
equal to the original polytope, do not constitute an efficient algorithm. Here we describe the central problem in carrying
out the enumeration efficiently after reaching a segment. We then discuss two procedures for enumerating extreme points, the
mukkadvayam checking procedure, and the nearest point procedure. We divide polytopes into two classes: Class 1 polytopes have
at least one extreme point satisfying the property that there is a hyperplane H through that extreme point such that every facet of the polytope incident at that extreme point has relative interior point
intersections with both sides of H; Class 2 polytopes have the property that every hyperplane through any extreme point has at least one facet incident at that
extreme point completely contained on one of its sides. We then prove that the procedures developed solve the problem efficiently
when the polytope belongs to Class 2. 相似文献
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Rolf Schneider 《Monatshefte für Mathematik》2007,150(3):241-247
If two convex bodies have the property that their orthogonal projections on any hyperplane have the same mean width and the
same Steiner point, then the bodies are identical. This result is proved in a stronger stability version. 相似文献
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Support vector machine (SVM) has attracted considerable attentions recently due to its successful applications in various
domains. However, by maximizing the margin of separation between the two classes in a binary classification problem, the SVM
solutions often suffer two serious drawbacks. First, SVM separating hyperplane is usually very sensitive to training samples
since it strongly depends on support vectors which are only a few points located on the wrong side of the corresponding margin boundaries. Second, the separating hyperplane is equidistant
to the two classes which are considered equally important when optimizing the separating hyperplane location regardless the
number of training data and their dispersions in each class. In this paper, we propose a new SVM solution, adjusted support
vector machine (ASVM), based on a new loss function to adjust the SVM solution taking into account the sample sizes and dispersions
of the two classes. Numerical experiments show that the ASVM outperforms conventional SVM, especially when the two classes
have large differences in sample size and dispersion. 相似文献
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A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or quadratic integer-relaxed subproblems are first solved to rapidly generate a tight linear relaxation of the original MINLP problem. After an initial overestimated set has been obtained the algorithm solves a sequence of mixed-integer linear programming or mixed-integer quadratic programming subproblems and refines the overestimated set by generating more supporting hyperplanes in each iteration. Compared to the extended cutting plane algorithm ESH generates a tighter overestimated set and unlike outer approximation the generation point for the supporting hyperplanes is found by a simple line search procedure. In this paper it is proven that the ESH algorithm converges to a global optimum for convex MINLP problems. The ESH algorithm is implemented as the supporting hyperplane optimization toolkit (SHOT) solver, and an extensive numerical comparison of its performance against other state-of-the-art MINLP solvers is presented. 相似文献
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Harm Pralle 《Geometriae Dedicata》2001,84(1-3):1-23
The complement of a geometric hyperplane of a generalized quadrangle is called an affine generalized quadrangle. Since a geometric hyperplane of a generalized quadrangle is either an ovoid or the perp of a point or a subquadrangle, there are three quite different classes of affine generalized quadrangles. The article proposes seven axioms (AQ1)–(AQ7) characterizing affine generalized quadrangles as point-line geometries. Certain subsets of the seven Axioms together with certain conditions distinguish what kind of hyperplane complement is realized. By just (AQ1)–(AQ6), finite affine generalized quadrangles are characterized completely. 相似文献
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Professors Dr. P. Marcotte G. Savard 《Mathematical Methods of Operations Research》1992,36(6):517-545
We consider the problem of determining a hyperplane that separates, as well as possible, two finite sets of points inR
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. We analyze two criteria for judging the quality of a candidate hyperplane (i) the maximal distance of a misclassified point to the hyperplane (ii) the number of misclassified points. In each case, we investigate the computational complexity of the corresponding mathematical programs, give equivalent formulations, suggest solution algorithms and present preliminary numerical results.Research supported by NSERC grants 5789 and 46405, the Academic Research Program of the Department of National Defense (Canada) and FCAR grant 91NC0510. (Québec). 相似文献
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For a convex program in a normed vector space with the objective function admitting the Gateaux derivative at an optimal solution, we show that the solution set consists of the feasible points lying in the hyperplane whose normal vector equals the Gateaux derivative. For a general continuous convex program, a feasible point is an optimal solution iff it lies in a hyperplane with a normal vector belonging to the subdifferential of the objective function at this point. In several cases, the solution set of a variational inequality problem is shown to coincide with the solution set of a convex program with its dual gap function as objective function, while the mapping involved can be used to express the above normal vectors.The research was supported by the National Science Council of the Republic of China. The authors are grateful to the referees for valuable comments and constructive suggestions. 相似文献