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21.
Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x
n)}, where {x
n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper. 相似文献
22.
A. Dax 《Journal of Optimization Theory and Applications》1990,64(2):429-432
This note suggests new ways for calculating the point of smallest Euclidean norm in the convex hull of a given set of points inR
n
. It is shown that the problem can be formulated as a linear least-square problem with nonnegative variables or as a least-distance problem. Numerical experiments illustrate that the least-square problem is solved efficiently by the active set method. The advantage of the new approach lies in the solution of large sparse problems. In this case, the new formulation permits the use of row relaxation methods. In particular, the least-distance problem can be solved by Hildreth's method. 相似文献
23.
Sun Hesheng 《偏微分方程(英文版)》1990,3(2)
In practical problems there appears higher-order equations of changing type([1]). But, there are only a few of papers concerning this type of equations ([2]-[6]). In this paper, the global existence of regular solutions to the Initial-boundary value problem for a class of higher-order system of equations of changing type with a strong nonlinear term is studied. 相似文献
24.
LiuYanyan WuJun 《分析论及其应用》2003,19(4):342-354
A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets. 相似文献
25.
Rafael O. Ruggiero Vladimir A. Rosas Meneses 《Bulletin of the Brazilian Mathematical Society》2003,34(2):263-274
In this paper, we show that the Pesin set of an expansive
geodesic flow in compact manifold with no conjugate points and
bounded asymptote coincides a.e with an open and dense set of
the unit tangent bundle. We also show that the set of hyperbolic
periodic orbits is dense in the unit tangent bundle. 相似文献
26.
Conditions for the uniform continuity of a family of weakly regular set functions defined on an algebra of subsets of a -topological space (T,) and taking values in an arbitrary topological space are found. 相似文献
27.
The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given referential coordinate set and a corresponding distance vector, sufficient and necessary conditions are presented for the existence of such a point that the distance vector can be realized. The location of the point (if it exists) given by the approaches in a linear manifold is independent of the coordinate system, and is only related to the referential coordinate set and the corresponding distance vector. An interesting phenomenon about the complexity of the EDM completion problem is described. Some properties about the uniqueness and the rigidity of the conformation for solutions to the EDM and PSD completion problems are presented. 相似文献
28.
The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large. 相似文献
29.
Roman Barták 《Annals of Operations Research》2003,118(1-4):101-119
Global constraints provide strong filtering algorithms to reduce the search space when solving large combinatorial problems. In this paper we propose to make the global constraints dynamic, i.e., to allow extending the set of constrained variables during search. We describe a generic dynamisation technique for an arbitrary monotonic global constraint and we compare it with the semantic-based dynamisation for the alldifferent constraint. At the end we sketch a dynamisation technique for non-monotonic global constraints. A comparison with existing methods to model dynamic problems is given as well. 相似文献
30.
C. Ratsch C. Anderson R. E. Caflisch L. Feigenbaum D. Shaevitz M. Sheffler C. Tiee 《Applied Mathematics Letters》2003,16(8):1165-1170
We adapt the level-set method to simulate epitaxial growth of thin films on a surface that consists of different reconstruction domains. Both the island boundaries and the boundaries of the reconstruction domains are described by different level-set functions. A formalism of coupled level-set functions that describe entirely different physical properties is introduced, where the velocity of each level-set function is determined by the value of the other level-set functions. 相似文献