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1.
A number of problems concerning sets of points in the plane are studied, e.g. establishing whether it contains a subset of size 4, which are the vertices of a square or rectangle. Both the problems of finding axis-parallel squares and rectangles, and arbitrarily oriented squares and rectangles are studied. Efficient algorithms are obtained for all of them. Furthermore, we investigate the generalizations tod-dimensional space, where the problem is to find hyperrectangles and hypercubes. Also, upper and lower bounds are given for combinatorial problems on the maxium number of subsets of size 4, of which the points are the vertices of a square or rectangle. Then we state an equivalence between the problem of finding rectangles, and the problem of findingK
2, 2 subgraphs in bipartite graphs. Thus we immediately have an efficient algorithm for this graph problem.This work was partially supported by the ESPRIT Basic Research Action No. 3075 (project ALCOM). Work of the second author was also supported by the Dutch Organisation for Scientific Research (N.W.O.). 相似文献
2.
曾云波 《高校应用数学学报(A辑)》1993,(4):339-350
本文表明,利用两个特征值问题的规范变换,不仅可以建立和它们相联系的势的约束之间以及相应的有限维Hamilton系统间的变换关系式,而且可以由一个可积系统的对合守恒积分导出另一个系统的守恒积分 相似文献
3.
A number of important problems in computational geometry are solved efficiently on 2- or 3-dimensional grids by means of scanline techniques. In the time complexity of solutions to the maximal elements and closure problems, a factor logn is substituted by loglogn, wheren is the number of elements. Next, by using a data structure introduced in the paper, the interval trie, previous solutions to the rectangle intersection and connected component problems are improved upon. Finally, a fast intersection finding algorithm for arbitrarily oriented line segments is presented. 相似文献
4.
R. Nozawa 《Applied Mathematics and Optimization》1999,40(1):1-18
Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and
noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized
the problems and called the generalized problems max-flow and min-cut problems of Strang's type. In this paper we formulate
a relaxed version of the min-cut problem of Strang's type and prove the existence of optimal solutions under some suitable
conditions. The conditions are essential. In fact, there is an example of the relaxed version which has no optimal solutions
if the conditions are not fulfilled. We give such an example in the final section.
Accepted 8 October 1998 相似文献
5.
Lou 《Applied Mathematics and Optimization》2008,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
6.
Riccardo Cambini Francesca Salvi 《Journal of Computational and Applied Mathematics》2009,233(2):492-501
Various classes of d.c. programs have been studied in the recent literature due to their importance in applicative problems. In this paper we consider a branch and reduce approach for solving a class of d.c. problems. Seven partitioning rules are analyzed and some techniques aimed at improving the overall performance of the algorithm are proposed. The results of a computational experience are provided in order to point out the performance effectiveness of the proposed techniques. 相似文献
7.
D. Han 《Applied Mathematics and Optimization》2002,45(1):63-74
The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever
the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as
structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating
direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just
makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results
to illustrate the efficiency of the method.
Accepted 4 May 2001. Online publication 19 October, 2001. 相似文献
8.
Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional
approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated
that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating
subspaces consisting of piecewise constant functions. Algorithms based on a primal—dual framework that exploit the structure
of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images
with very high noise.
Accepted 29 March 1998 相似文献
9.
10.
Lou 《Applied Mathematics and Optimization》2003,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
11.
Dong-hui Li Jin-ping Zeng 《计算数学(英文版)》1998,16(1):40-50
1.IntroductionConsiderthefollowingnonlinearcomplementarityproblemsNCP(F)offindinganxER",suchthatwhereFisamappingfromR"intoitself.ItisanimportantformofthefollowingvariationalinequalityVI(F,X)offindinganxEX,suchthatwhereXCReisaclosedconvexset.WhenX=R7,(1.1)… 相似文献
12.
N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1990,64(3):573-594
In this paper, we examine relaxed control systems governed by evolution inclusions in a separable Banach space. First, we establish the existence of admissible trajectories, correcting an earlier result of Ahmed. Then, we obtain a compactness result for the set of admissible trajectories. Using this compactness result, we prove the existence of optimal solutions for optimal control problems; furthermore, we show that the values of the original and relaxed problems are equal. Finally, we show that the original trajectories are dense in the set of relaxed trajectories. An example is worked out.This research was supported by NSF Grant No. DMS-86-02313. 相似文献
13.
Stanislav Uryas'ev 《Numerical Functional Analysis & Optimization》2013,34(7-8):827-841
Formulae for differentiation with respect to the parameter of an integral over the set given by an inclusion are proposed. The case with bounded and unbounded set is discussed. Such formulae can be used for differentiation of probability functions. An algorithm for solving chance constrainted optimization problems is considered. 相似文献
14.
W. M. Turski 《BIT Numerical Mathematics》1988,28(3):473-486
Various manifestations of the time-as-a-proxy phenomenon in specification of computing problems are considered. It is argued that unless the time-related considerations constitute an essential part of natural (physical) problems, safer specifications are obtained from avoiding short-cuts offered by introduction of time-related notions. This methodological principle is illustrated by examples from several fields: digital control and simulation, design of operator's interface and communication protocols.Dedicated to Peter Naur on the occasion of his 60th birthday 相似文献
15.
C. Léonard 《Applied Mathematics and Optimization》2001,44(3):273-297
We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints.
Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This
equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class
of generalized Fredholm integral equations. In particular, our abstract results are applied to marginal problems for stochastic
processes. Such problems naturally arise from the probabilistic approaches to quantum mechanics.
Accepted 26 March 2001. Online publication 19 July 2001. 相似文献
16.
莫嘉琪 《数学物理学报(A辑)》2003,23(3):374-378
研究了具有非线性反应扩散方程奇摄动问题。在适当的条件下,利用微分不等式理论,讨论了当退化问题具有两个相交解时,原初始边值问题解的渐近性态。
相似文献
17.
Solving a Class of Linearly Constrained Indefinite Quadratic Problems by D.C. Algorithms 总被引:3,自引:0,他引:3
Linearly constrained indefinite quadratic problems play an important role in global optimization. In this paper we study d.c. theory and its local approachto such problems. The new algorithm, CDA, efficiently produces local optima and sometimes produces global optima. We also propose a decomposition branch andbound method for globally solving these problems. Finally many numericalsimulations are reported. 相似文献
18.
几类考虑有限理性平衡问题解的稳定性 总被引:2,自引:0,他引:2
对Ky Fan点问题定义了理性函数,证明了大多数的KyFan点问题(在Baire分类意义上)都是结构稳定的,对$\varepsilon$-平衡也都是鲁棒的.作为应用,还给出了Nash平衡问题和变分不等式问题的稳定性结论. 相似文献
19.
Walter Alt 《Numerical Functional Analysis & Optimization》2013,34(3-4):201-224
This paper investigates local convergence properties of the Lagrange-Newton method for optimization problems in reflexive Banach spaces. Sufficient conditions for quadratic convergence of optimal solutions and Lagrange multipliers are given. The results are applied to optimal control problems. 相似文献