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51.
Philip E. Gill Walter Murray Michael A. Saunders Margaret H. Wright 《Mathematical Programming》1989,45(1-3):437-474
A procedure is described for preventing cycling in active-set methods for linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance of infeasibilities in all variables, and maintenance of a working feasibility tolerance that increases over a long sequence of iterations. The additional work per iteration is nominal, and stalling cannot occur with exact arithmetic. The method appears to be reliable, based on computational results for the first 53 linear programming problems in theNetlib set.The material contained in this report is based upon research supported by the Air Force Office of Scientific Research Grant 87-01962; the U.S. Department of Energy Grant DE-FG03-87ER25030; National Science Foundation Grants CCR-8413211 and ECS-8715153; and the Office of Naval Research Contract N00014-87-K-0142. 相似文献
52.
The Revised Primal Simplex algorithm, in its simplest form, has no defence against degeneracy. Various forms of the perturbation method are usually effective, but most offer no guarantee of avoiding all degeneracy, and can lead to numerical difficulties. This paper presents a method that avoids cycling and circling by taking a dual approach.The degenerate subproblem consists of all the original variables, but only the degenerate transformed constraints. The current primal objective, which may be mixed, is used. This subproblem may be solved using the dual simplex algorithm, starting from the current dual infeasible solution, and with a zero dual objective. If the dual algorithm terminates optimally then the whole problem is optimal (subject to primal feasibility). Otherwise the final solution provides a non-basic direction which improves the value of the mixed primal objective and moves away from the degenerate vertex. A purification algorithm then renders the solution basic and further improves the mixed objective. 相似文献
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54.
Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that, for a class of second order linearly degenerate dispersionless integrable PDEs, the corresponding characteristic integrals are parametrised by points on the Veronese variety. 相似文献
55.
The CANDECOMP/PARAFAC (CP) model is a well known and frequently used tool for extracting substantial information from a three‐way data array. It has several useful characteristics and usually gives meaningful insights about the underlying structure of the data. However, in some cases it has a ‘strange’ behaviour suffering from the so‐called ‘degenerate solutions’, i.e. solutions where the components show a diverging pattern and are meaningless. Several authors have investigated the causes of degeneracy concluding that the phenomenon is due to a lack of minimum of the loss function. In this paper, we study the degeneracy of CP limiting our attention to the two‐component case. The study is done by introducing a canonical form, called 2DR, which is ‘weakly degeneracy revealing’. On the ground of this framework, degeneracy is studied along with some of the remedies proposed in the literature by using a Tucker3 model having a core in the 2DR form. The analysis gives new insights about the behaviour of the CP model and suggests new ideas on how to deal with degeneracy. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
56.
We consider the localization game played on graphs, wherein a set of cops attempt to determine the exact location of an invisible robber by exploiting distance probes. The corresponding optimization parameter for a graph G is called the localization number and is written as ζ(G). We settle a conjecture of Bosek et al by providing an upper bound on the chromatic number as a function of the localization number. In particular, we show that every graph with ζ(G) ≤ k has degeneracy less than 3k and, consequently, satisfies χ(G) ≤ 3ζ(G). We show further that this degeneracy bound is tight. We also prove that the localization number is at most 2 in outerplanar graphs, and we determine, up to an additive constant, the localization number of hypercubes. 相似文献
57.
58.
K. Lai W. Pan D.C. Tsui S. Lyon M. Mühlberger F. Schffler 《Physica E: Low-dimensional Systems and Nanostructures》2006,34(1-2):176
Tilted field magnetotransport study was performed in a two-valley strained Si quantum well and hysteretic diagonal resistance spikes were observed near the coincidence angles. The spike around filling factor ν=3 develops into a giant feature when it moves to the high-field edge of the quantum Hall (QH) state and quenches for higher tilt angles. When the spike is most prominent, its peak resistance is temperature independent from T20 mK up to 0.3 K, which is different from the critical behavior previously reported near the Curie temperature of the QH ferromagnet in AlAs quantum wells. Our data suggest a strong interplay between spins and valleys near the coincidence. 相似文献
59.
本文评述了遗传密码的进化有关的物理问题。主要讨论了 :1 )从进化稳定性的观点研究遗传密码的简并规则 ,证明了现有密码表中多重态的简并规则是突变危险性极小的 ;2 )从进化稳定性的观点研究了遗传密码表中氨基酸和终止密码子的排布 ,导出了总体突变危险性极小的表 ,并证明了标准密码表是在某些约束 (这些约束反映了密码形成时期的初始条件 )下总体突变危险性极小的表 ;3)密码表中 2 0种氨基酸和终止密码简并度的分布 ,以及改变简并度条件下密码反常的出现 相似文献
60.