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951.
We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization
to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic
growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, Luo and Tseng (SIAM J. Optim.
13, 1098–1119, 2003) under the assumption of convexity, the Slater constraint qualification, and a strong second-order sufficient condition.
We obtain a new local convergence result, which complements the above (it is neither stronger nor weaker): we prove primal-dual
quadratic convergence under the linear independence constraint qualification, strict complementarity, and a second-order sufficiency
condition. Additionally, our results apply to variational problems beyond the optimization case. Finally, we provide a necessary
and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition.
Research of the second author is partially supported by CNPq Grants 300734/95-6 and 471780/2003-0, by PRONEX–Optimization,
and by FAPERJ. 相似文献
952.
Satya Prakash Pranav Kumar B.V.N.S. Prasad Anuj Gupta 《European Journal of Operational Research》2008
A cost–time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each destination is to be met from one source only; however a source can supply to any number of destinations subject to the availability of the commodity at it. Two new algorithms are provided to obtain the set of Pareto optimal solutions of this problem. This work extends and generalizes the work related to single-objective and prioritized two-objective bulk transportation problems done in the past while providing flexibility in decision making. 相似文献
953.
The noncommutative Singer-Wermer conjecture states that every linear (possibly unbounded) derivation on a (possibly noncommutative) Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left θ-derivations. 相似文献
954.
Mathematical Notes - 相似文献
955.
We correct an error in the statement of Theorem 8 in [1].
Received: January 3, 2001 / Accepted: February 26, 2001?Published online May 18, 2001 相似文献
956.
VPAStab(J,L) denotes an iterative method designed to give an accurate numerical solution of a large sparse system of linear equations. The iteration comprises L-steps and possibly jump-steps. An L-step involves stabilisation (minimisation) over an L-dimensional subspace following L levels of vector-Padé approximation. A jump-step (look-ahead stage) avoids near-breakdowns by jumping past them by J levels simultaneously. A numerical implementation of VPAStab(2,L) is considered in the context of some well-known examples. 相似文献
957.
958.
T. Binder L. Blank W. Dahmen W. Marquardt 《Journal of Optimization Theory and Applications》2001,111(3):529-551
Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary. 相似文献
959.
Marie-Christine Plateau 《4OR: A Quarterly Journal of Operations Research》2008,6(2):187-190
This is a summary of the author’s PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the
CNAM, Paris (Conservatoire National des Arts et Métiers). The thesis is written in French and is available from http://www.cedric.cnam.fr/PUBLIS/RC1115.
This work deals with exact solution methods based on reformulations for quadratic 0–1 programs under linear constraints. These
problems are generally not convex; more precisely, the associated continuous relaxation is not a convex problem. We developed
approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation.
The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization
problems.
相似文献
960.
We continue the study of G. Castelnuovo on the group of birational transformations of the complex plane that fix each point
of a curve of genus > 1 ; we use adjoint linear system of the curve as Castelnuovo does. We prove that these groups are abelian,
and that these are either finite, of order 2 or 3, or conjuguate to a subgroup of the de Jonquières group. We show also that
these results do not generalise to curves of genus ≤ 1.
*Partiellement soutenu par le CNPq-Brasil et la Section de Mathématiques de l'Université de Genève. 相似文献