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1.
Efficient Arithmetic on Koblitz Curves   总被引:24,自引:0,他引:24  
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation.Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.  相似文献
2.
For the second order boundary value problem, , , , where growth conditions are imposed on which yield the existence of at least three symmetric positive solutions.

  相似文献

3.
This article presents a probabilistic technique to diversify, intensify, and parallelize a local search adapted for solving vehicle routing problems. This technique may be applied to a very wide variety of vehicle routing problems and local searches. It is shown that efficient first-level tabu searches for vehicle routing problems may be significantly improved with this technique. Moreover, the solutions produced by this technique may often be improved by a postoptimization technique presented in this article, too. The solutions of nearly forty problem instances of the literature have been improved.  相似文献
4.
On the singular set of stationary harmonic maps   总被引:15,自引:0,他引:15  
LetM andN be compact riemannian manifolds, andu a stationary harmonic map fromM toN. We prove thatH n−2 (Σ)=0, wheren=dimM and Σ is the singular set ofu. This is a generalization of a result of C. Evans [7], where this is proved in the special caseN is a sphere. We also prove that, ifu is a weakly harmonic map inW 1,n (M, N), thenu is smooth. This extends results of F. Hélein for the casen=2, or the caseN is a sphere ([9], [10]).  相似文献
5.
Bilevel programming: A survey   总被引:14,自引:0,他引:14  
This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.Received: April 2005, Revised: May 2005, AMS classification: 90C05, 90C11, 90C20, 90C27, 90C3D, 65K05  相似文献
6.
Auxiliary problem principle and decomposition of optimization problems   总被引:14,自引:0,他引:14  
The auxiliary problem principle allows one to find the solution of a problem (minimization problem, saddle-point problem, etc.) by solving a sequence of auxiliary problems. There is a wide range of possible choices for these problems, so that one can give special features to them in order to make them easier to solve. We introduced this principle in Ref. 1 and showed its relevance to decomposing a problem into subproblems and to coordinating the subproblems. Here, we derive several basic or abstract algorithms, already given in Ref. 1, and we study their convergence properties in the framework of i infinite-dimensional convex programming.  相似文献
7.
Auxiliary problem principle extended to variational inequalities   总被引:13,自引:0,他引:13  
The auxiliary problem principle has been proposed by the author as a framework to describe and analyze iterative optimization algorithms such as gradient or subgradient as well as decomposition/coordination algorithms (Refs. 1–3). In this paper, we extend this approach to the computation of solutions to variational inequalities. In the case of single-valued operators, this may as well be considered as an extension of ideas already found in the literature (Ref. 4) to the case of nonlinear (but still strongly monotone) operators. The case of multivalued operators is also investigated.This research has been supported by the Centre National de la Recherche Scientifique (ATP Complex Technological Systems) and by the Centre National d'Études des Télécommunications (Contract No. 83.5B.034.PAA). It has been conducted partly while the author was visiting the Department of Electrical Engineering of the Pontificia Catholic University of Rio de Janeiro in July–August 1984 under the CAPES/COFECUB scientific exchange program.  相似文献
8.
We present a branch and cut algorithm that yields in finite time, a globally ε-optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizations (cuts), depending on one to three parameters, are detailed. For each class, we show how to select the best member with respect to a precise criterion. The cuts introduced at any node of the tree are valid in the whole tree, and not only within the subtree rooted at that node. In order to enhance the computational speed, the structure created at any node of the tree is flexible enough to be used at other nodes. Computational results are reported that include standard test problems taken from the literature. Some of these problems are solved for the first time with a proof of global optimality. Received December 19, 1997 / Revised version received July 26, 1999?Published online November 9, 1999  相似文献
9.
On the Dirichlet problem for Hessian equations   总被引:12,自引:0,他引:12  
10.
Everywhere discontinuous harmonic maps into spheres   总被引:12,自引:0,他引:12  
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