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201.
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization 总被引:7,自引:0,他引:7
In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The
algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X=RR
T
. The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results
concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems
are also presented.
Received: March 22, 2001 / Accepted: August 30, 2002 Published online: December 9, 2002
Key Words. semidefinite programming – low-rank factorization – nonlinear programming – augmented Lagrangian – limited memory BFGS
This research was supported in part by the National Science Foundation under grants CCR-9902010, INT-9910084, CCR-0203426
and CCR-0203113 相似文献
202.
Curtis T. Mcmullen 《Acta Mathematica》2003,191(2):191-223
203.
Sigal Leviatan 《International Journal of Game Theory》2003,31(3):383-410
The consistent value is an extension of the Shapley value to the class of games with non-transferable utility.? In this paper,
the consistent value will be characterized for market games with a continuum of players of two types. We will show that for
such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between
the two concepts.
Received: October 1998
RID="*"
ID="*" This thesis was completed under the supervision of Professor Sergiu Hart, The Center for Rationality and Interactive
Decision Theory, Department of Mathematics, Department of Economics, The Hebrew University of Jerusalem. I would like to thank
Professor Hart for introducing me to this area of research, for his help and guidance, and, especially, for all his patience.? I
would also like to thank Michael Borns for improving the style, and an anonymous referee for helpful comments. 相似文献
204.
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces. 相似文献
205.
206.
Roberto Montemanni 《4OR: A Quarterly Journal of Operations Research》2003,1(3):257-260
A survey of the results described in the authors PhD thesis (Montemanni 2001) is presented. The thesis, which was supervised by Prof. Derek H. Smith and Dr. Stuart M. Allen, has been defended in January 2002 at the University of Glamorgan (U.K.). The thesis proposes new heuristic algorithms, based on well-known meta-heuristic paradigms, and new lower bounding techniques, based on linear programming, for the fixed spectrum frequency assignment problem.Received: May 2003, Revised: May 2003, AMS classification:
90C27, 90C59,05C90, 90C05Roberto Montemanni: Present address: Istituto Dalle Molle di Studi sullIntelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno-Lugano, Switzerland (e-mail: roberto@idsia.ch) 相似文献
207.
208.
Summary. We consider the Maxwell equations in a domain with Lipschitz boundary and the boundary integral operator A occuring in the Calderón projector. We prove an inf-sup condition for A using a Hodge decomposition. We apply this to two types of boundary value problems: the exterior scattering problem by a perfectly conducting body, and the dielectric problem with two different materials in the interior and exterior domain. In both cases we obtain an equivalent boundary equation which has a unique solution. We then consider Galerkin discretizations with Raviart-Thomas spaces. We show that these spaces have discrete Hodge decompositions which are in some sense close to the continuous Hodge decomposition. This property allows us to prove quasioptimal convergence of the resulting boundary element methods.
Mathematics Subject Classification (2000):65N30 相似文献
209.
We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field
goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki
[4].
Received September 10, 2001; in revised form April 5, 2002 相似文献
210.
TangLin YangDachun 《分析论及其应用》2003,19(1):1-13
Let n≥2. In this paper, the author establishes the L^2 (R^n)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hypergeometric functions and congqucnt hypergeometric funtions. 相似文献