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本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优. 相似文献
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一、专题的背景与分析
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闵行区的沪闵路─春申路口是交通特别拥挤的交叉路口之一.家住莘庄地区的同学有一个共同的感受,在他们到校或回家路上必经的沪闵路─春申路口时常遇到塞车现象.…… 相似文献
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"牛吃草"问题又称为消长问题,是17世纪英国伟大的科学家牛顿提出来的.典型牛吃草问题的条件是假设草的生长速度固定不变,不同头数的牛吃光同一片草地所需的天数各不相同,求若干头牛吃这片草地可以吃多少天.由于吃的天数不同,草又是天天在生长的,所以草的存量随吃的天数不断地变化.…… 相似文献
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导数作为大学的重要内容,进入中学数学教材后,给传统的内容注入了生机与活力,为中学数学命题的研究提供了新视角,新方法.由于导数是研究函数性质的一个很好的工具,它的用途十分广泛,它在解决函数、不等式、解析几何等问题有独到的功能.因此,近几年的高考正逐年加大对导数问题的考查力度,本文通过对07年全国各地高考题的整理和分析寻找命题规律,希望能对今后的教学提供一点复习思路.…… 相似文献
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利用极值理论来考虑上证综指收益率的尾部.为了选择合理的超越门限,采用平均剩余函数和De-Haan矩估计相结合的方法.在学生t分布和广义误差分布的新患假设下,用GARCH和EGARCH新息的ARMA模型拟合指数收益率,并且使用极值理论的极大似然方法估计模型残差的尾指,估计结果表明收益率的尾指和模型的残差尾指基本一致. 相似文献
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In this note, the set of weak Pareto solutions of a multicriteria linear programming problem (MCLP, for short) is proved to be a set of weak sharp minima for another residual function of MCLP, i.e., the minimum of the natural residual functions of finitely many scalarization problems of MCLP, which is less than the natural residual function of MCLP. This can be viewed as a slight improvement of a result due to Deng and Yang. Some examples are given to illustrate these results. 相似文献
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We show that penalized functions of the Fischer–Burmeister and the natural residual functions defined on symmetric cones are
complementarity functions. Boundedness of the solution set of a symmetric cone complementarity problem, based on the penalized
natural residual function, is proved under monotonicity and strict feasibility. The proof relies on a trace inequality on
Euclidean Jordan algebras. 相似文献
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Shenglong Hu Jie Wang Zheng-Hai Huang 《Journal of Optimization Theory and Applications》2018,179(3):983-1000
In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standard violation measure of the polynomial equalities and inequalities. These fractional local error bounds are given with explicit exponents. A fractional local error bound with an explicit exponent via the natural residual function is new in the tensor/polynomial complementarity problems literature. The other fractional local error bounds take into account the sparsity structures, from both the algebraic and the geometric perspectives, of the third-order tensor in a quadratic complementarity problem. They also have explicit exponents, which improve the literature significantly. 相似文献
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Growth behavior of a class of merit functions for the nonlinear complementarity problem 总被引:3,自引:0,他引:3
P. Tseng 《Journal of Optimization Theory and Applications》1996,89(1):17-37
When the nonlinear complementarity problem is reformulated as that of finding the zero of a self-mapping, the norm of the selfmapping serves naturally as a merit function for the problem. We study the growth behavior of such a merit function. In particular, we show that, for the linear complementarity problem, whether the merit function is coercive is intimately related to whether the underlying matrix is aP-matrix or a nondegenerate matrix or anR
o-matrix. We also show that, for the more popular choices of the merit function, the merit function is bounded below by the norm of the natural residual raised to a positive integral power. Thus, if the norm of the natural residual has positive order of growth, then so does the merit function.This work was partially supported by the National Science Foundation Grant No. CCR-93-11621.The author thanks Dr. Christian Kanzow for his many helpful comments on a preliminary version of this paper. He also thanks the referees for their helpful suggestions. 相似文献
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Equivalence of the generalized complementarity problem to differentiable unconstrained minimization 总被引:4,自引:0,他引:4
We consider an unconstrained minimization reformulation of the generalized complementarity problem (GCP). The merit function introduced here is differentiable and has the property that its global minimizers coincide with the solutions of GCP. Conditions for its stationary points to be global minimizers are given. Moreover, it is shown that the level sets of the merit function are bounded under suitable assumptions. We also show that the merit function provides global error bounds for GCP. These results are based on a condition which reduces to the condition of the uniform P-function when GCP is specialized to the nonlinear complementarity problem. This condition also turns out to be useful in proving the existence and uniqueness of a solution for GCP itself. Finally, we obtain as a byproduct an error bound result with the natural residual for GCP.We thank Jong-Shi Pang for his valuable comments on error bound results with the natural residual for the nonlinear complementarity problem. We are also grateful to the anonymous referees for some helpful comments. The research of the second author was supported in part by the Science Research Grant-in-Aid from the Ministry of Education, Science, and Culture, Japan. 相似文献
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We investigate a one-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) which is
closely related to the popular Fischer–Burmeister (FB) merit function and natural residual merit function. In fact, it will
reduce to the FB merit function if the involved parameter τ equals 2, whereas as τ tends to zero, its limit will become a multiple of the natural residual merit function. In this paper, we show that this
class of merit functions enjoys several favorable properties as the FB merit function holds, for example, the smoothness.
These properties play an important role in the reformulation method of an unconstrained minimization or a nonsmooth system
of equations for the SOCCP. Numerical results are reported for some convex second-order cone programs (SOCPs) by solving the
unconstrained minimization reformulation of the KKT optimality conditions, which indicate that the FB merit function is not
the best. For the sparse linear SOCPs, the merit function corresponding to τ=2.5 or 3 works better than the FB merit function, whereas for the dense convex SOCPs, the merit function with τ=0.1, 0.5 or 1.0 seems to have better numerical performance. 相似文献
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A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity
function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the
penalized Fischer–Burmeister function for symmetric cone complementarity problems. We show that this class of functions is
indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity
functions is coercive. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(11):3299-3305
A popular approach to solving the complementarity problem is to reformulate it as an equivalent system of smooth equations via a smoothing complementarity function. In this paper, first we propose a new class of smoothing complementarity functions, which contains the natural residual smoothing function and the Fischer–Burmeister smoothing function for symmetric cone complementarity problems. Then we give some unified formulae of the Fréchet derivatives associated with Jordan product. Finally, the derivative of the new proposed class of smoothing complementarity functions is deduced over symmetric cones. 相似文献
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Deren Han 《Journal of Mathematical Analysis and Applications》2007,336(1):727-737
One of the popular solution methods for the complementarity problem over symmetric cones is to reformulate it as the global minimization of a certain merit function. An important question to be answered for this class of methods is under what conditions the level sets of the merit function are bounded (the coerciveness of the merit function). In this paper, we introduce the generalized weak-coerciveness of a continuous transformation. Under this condition, we prove the coerciveness of some merit functions, such as the natural residual function, the normal map, and the Fukushima-Yamashita function for complementarity problems over symmetric cones. We note that this is a much milder condition than strong monotonicity, used in the current literature. 相似文献
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Xin-He Miao 《Numerical Functional Analysis & Optimization》2013,34(5):507-523
In this article, we consider the Lorentz cone complementarity problems in infinite-dimensional real Hilbert space. We establish several results that are standard and important when dealing with complementarity problems. These include proving the same growth of the Fishcher–Burmeister merit function and the natural residual merit function, investigating property of bounded level sets under mild conditions via different merit functions, and providing global error bounds through the proposed merit functions. Such results are helpful for further designing solution methods for the Lorentz cone complementarity problems in Hilbert space. 相似文献