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61.
62.
The projective method for solving linear matrix inequalities 总被引:2,自引:0,他引:2
Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving
an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest
in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs
with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical
arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is
provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed. 相似文献
63.
We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1. 相似文献
64.
The number of trials that is required by an algorithm to produce a given fraction of the problem solutions with a specified level of confidence is analyzed. The analysis indicates that the number of trials required to find a large fraction of the solutions rapidly decreases as the number of solutions obtained on each trial by an algorithm increases. In applications where multiple solutions are sought, this decrease in the number of trials could potentially offset the additional computational cost of algorithms that produce multiple solutions on a single trial. The analysis framework presented is used to compare the efficiency of a homotopy algorithm to that of a Newton method by measuring both the number of trials and the number of calculations required to obtain a specified fraction of the solutions. 相似文献
65.
Wolfgang Kirmse 《Angewandte Chemie (International ed. in English)》1997,36(11):1164-1170
Alkenylidenes R2C?C: (= alkylidene carbenes) undergo regio- and stereoselective intramolecular C? H insertion reactions that are excellently suited for the synthesis of cyclopentenes. The 1, 2-shifts occurring with R?H and R?Ar are useful for the preparation of alkynes. Alkenylidenes are efficiently generated from carbonyl compounds by diazomethylation, from vinyl halides by α-elimination, from alkynyliodonium salts by addition of nucleophiles, and from alkynes by retro-1, 2-shifts. Specific applications of the various methods, particularly in the synthesis of natural products, are discussed. 相似文献
66.
威布尔分布是描述部件寿伞的一种极为主要的分布,本文对确定威布尔分布的三参数,给出了一种试探性算法,方法简单、实用。 相似文献
67.
L. Contesse-Becker 《Journal of Optimization Theory and Applications》1993,79(2):273-310
In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile). 相似文献
68.
The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper. 相似文献
69.
何先平 《太原师范学院学报(自然科学版)》2006,5(4):28-29,85
中国的经济发展主要存在着“东部”与“西部”的差距,文章利用聚类分析对我国部分省、市、自治区共28个样本进行分类,并加以分析. 相似文献
70.
Daniel Maerten 《Annals of Global Analysis and Geometry》2007,32(4):391-414
We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact
and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary,
dimensionless geometric constants and some normalized Sobolev ratio. 相似文献