Necessary Condition for a Strong Relative Minimum for Singular Optimal Control

A necessary condition is developed for a strong relative minimum for a first-order singular optimal control. It is shown that the strong condition is identical with the existing weak condition, namely, the generalized Legendre-Clebsch condition. It is conjectured that the strong condition for a second-order singular control will be the same as the corresponding weak condition.     

A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

We establish a sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. The sufficient condition relates to a sufficient condition for the weak stability of the fluid networks that correspond to the queueing networks under consideration. In addition, we establish a necessary condition for the network to have a continuous diffusion limit; the necessary condition is to require a reflection matrix (of dimension equal to the number of stations) to be completely-S. When applied to some examples, including generalized Jackson networks, single station multiclass queues, first-buffer-first-served re-entrant lines, a two-station Dai–Wang network and a three-station Dumas network, the sufficient condition coincides with the necessary condition.     

Mixed,componentwise condition numbers and small sample statistical condition estimation of Sylvester equations

We present a componentwise perturbation analysis for the continuous‐time Sylvester equations. Componentwise, mixed condition numbers and new perturbation bounds are derived for the matrix equations. The small sample statistical method can also be applied for the condition estimation. These condition numbers and perturbation bounds are tested on numerical examples and compared with the normwise condition number. The numerical examples illustrate that the mixed condition number gives sharper bounds than the normwise one. Copyright © 2011 John Wiley & Sons, Ltd.     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。     

COMPONENTWISE CONDITION NUMBERS FOR GENERALIZED MATRIX INVERSION AND LINEAR LEAST SQUARES

We present componentwise condition numbers for the problems of Moore-Penrose generalized matrix inversion and linear least squares. Also, the condition numbers for these condition numbers are given.     

KKT系统结构条件数与条件数的比较

本文讨论Karush-Kuhn_Tucker(KKT)系统的条件数．首先利用单参数展开方法建立了Byers型不等式,然后讨论结构条件数与条件数的定性比较,结果表明,在极端情形,条件数与结构条件数之比可以任意大．     

On global quadratic growth condition for min-max optimization problems with quadratic functions

Second-order sufficient condition and quadratic growth condition play important roles both in sensitivity and stability analysis and in numerical analysis for optimization problems. In this article, we concentrate on the global quadratic growth condition and study its relations with global second-order sufficient conditions for min-max optimization problems with quadratic functions. In general, the global second-order sufficient condition implies the global quadratic growth condition. In the case of two quadratic functions involved, we have the equivalence of the two conditions.     

关于模糊拟阵的独立子集套和独立集函数

本文的研究方法主要是将模糊拟阵问题转化为普通拟阵问题来研究的方法。本文首先建立独立子集套概念,并使用这个概念和独立集函数概念构建了闭模糊拟阵的充要条件和模糊独立集的充要条件;然后,本文仔细分析了模糊基的性质,找到了一个使用独立子集套和独立集函数来描述的模糊基的充要条件;最后,利用模糊基的这个充要条件提出并证明了闭正规模糊拟阵的充要条件。     

Comparison between exact thermal boundary condition and harmonic mean conductivity condition at the solid–fluid interface for finite thickness shrouded non-isothermal fin array

A numerical study is made comparing the exact thermal boundary condition and a harmonic mean conductivity condition at the solid–fluid interface for a finite thickness shrouded non-isothermal fin array. Results highlight that there exists a significant deviation of pressure drop across the length of the fin for the exact thermal boundary condition, which is as high as 20% as compared to that obtained using the harmonic mean conductivity condition. The exact thermal boundary condition forecasts relatively more non-isothermal fin as compared to a harmonic mean conductivity condition. The greater the fin spacing the larger the non-isothermal behavior of the fin and it also depends upon Grashof number as well as inlet fluid velocity. The larger the Grashof number the greater is the non-isothermal behavior of fin. The greater the inlet velocity, the larger is the non-isothermal behavior of fin. Bulk fluid temperature is over predicted by as much as 13% by the harmonic mean conductivity condition for larger fin spacing with highest Grashof number coupled with larger velocity. This deviation is only 6% for smaller fin spacing. Overall Nusselt number is over predicted for the harmonic mean conductivity condition as compared to exact thermal boundary condition. This over prediction is limited to about 8%.     

A criterion for checking if a convex set belongs to the union of a finite number of convex sets

A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.     

A new necessary condition for optimality of systems with time delay

A new necessary condition for optimality of nonsingular control problems with time delay is developed. This condition accounts for the interaction of the different delays in the control vector. A necessary condition for optimality of singular control problems with time delay is also obtained as a corollary of the new condition.     

A condition for diagonalization modulo arbitrary norm ideals

We give a spectral condition which is sufficient for the simultaneous diagonalization of a commuting tuple of self-adjoint operators modulo a given norm ideal. For diagonalization modulo certain norm ideals this condition is also necessary, while for other norm ideals this condition seems to be close to being necessary. Moreover, this condition is easy to verify in applications.     

Optimal control with delays and mixed initial condition

This paper studies optimal control problems with unfixed initial instant for systems described by differential equations with variables delays and mixed initial condition. The mixed initial condition means that at the initial instant of time, some coordinates of the trajectory do not coincide with the corresponding coordinates of the initial function (a discontinuous part of the initial condition), whereas the others coincide (a continuous part of the initial condition). The authors prove necessary optimality conditions for the control and the initial function for the initial and final instants of time. From these conditions should be isolated the condition for the initial instant containing the effect of mixed initial condition. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 58, Optimal Control, 2008.     

一类非线性时滞系统与时滞相关的H_∞控制

考虑一类非线性时滞系统的H∞控制.并对非线性项给出了一个新假设,在其假设下利用线性矩阵不等式方法得到了与时滞相关的H∞控制,同时也得到了该类非线性时滞系统鲁棒镇定的充分条件.     

Topological and metrical conditions for Collet-Eckmann unimodal maps

1. IntroductionColletEchazann maps (i.e. every ColletEckmann maP has positive lower LyaPunovexponent at the critical value) play a very important role in the study of one dimensionaldynamical systems. They have very good metricaI and ergodic properties[ll2], for example,every COllet-Eckmann map admits an absolutely cootinuous invariani m.asur.[1].In I3,4] Benedicks and Carleson proved that Collet-Eckmann maps are abundant in theso-caJled quadratic family which is a typical family of one …     

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.     

THE ASYMPTOTIC PROPERTIES OF SUPERCRITICAL BISEXUAL GALTON-WATSON BRANCHING PROCESSES WITH IMMIGRATION OF MATING UNITS

In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L1 convergence are given for the process with the suitably normed condition.     

A sufficient condition for a graph to contain three disjoint 1-factors

Ore derived a sufficient condition for a graph to contain a Hamiltonian cycle. We obtain a sufficient condition, similar to Ore's condition, for a graph to contain a Hamiltonian cycle and a 1-factor which are edge disjoint.     

二维不可压缩磁流体方程边界层分离的条件

该文研究了二维不可压缩磁流体方程的解,其中要求磁流体的速度满足Dirichlet边界条件、磁场在边界上的值与时间无关. 利用Taylor展开式和不可压缩流的结构分歧理论, 得到了磁流体方程发生边界层分离的条件, 它取决于外力、初值和磁场在边界上的取值, 并且该条件可以预测磁流体边界层分离发生的时间与地点.     

An approximate strong KKT condition for multiobjective optimization

In this paper, we introduce a sequential approximate strong Karush–Kuhn–Tucker (ASKKT) condition for a multiobjective optimization problem with inequality constraints. We show that each local efficient solution satisfies the ASKKT condition, but weakly efficient solutions may not satisfy it. Subsequently, we use a so-called cone-continuity regularity (CCR) condition to guarantee that the limit of an ASKKT sequence converges to an SKKT point. Finally, under the appropriate assumptions, we show that the ASKKT condition is also a sufficient condition of properly efficient points for convex multiobjective optimization problems.