A new approach to the busy period of the M/M/1 queue

In this paper, we provide a new approach to the computation of the Laplace transform of the length of the busy period of the M/M/1 queue with constrained workload (finite dam), without the use of complex analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

On local convergence of sequential quadratically-constrained quadratic-programming type methods,with an extension to variational problems

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.     

Sample average approximation of expected value constrained stochastic programs

We propose a sample average approximation (SAA) method for stochastic programming problems with expected value constraints. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). We provide a convergence analysis and a statistical validation scheme for the proposed method.     

New algorithm for optimal parameter estimation with linear constraints

This paper presents a new algorithm for optimal parameter estimation problems with linear constraints. The algorithm developed is based on least absolute-value approximations. The problem is solved first using a least-error-square technique, where we add to the cost function the equality constraints via Lagrange multipliers, to obtain a good estimate for the residuals of the measurements, having gained this information, we choose a number of measurements with the smallest residuals. This number equals the number of parameters to be estimated minus the number of constraints. Using these measurements together with the constraints, we obtain a number of observations equal to the number of parameters to be estimated. By using this technique, we show that there is no need to either iterate or use linear programming to obtain the estimation.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant A4146.     

一类具有连续变量的二阶非线性阻尼差分方程的振动准则

考虑了一类具有连续变量的二阶非线性阻尼差分方程,利用积分变换和广义R iccati变换,给出了此类方程的振动准则.     

Image space approach to penalty methods

In this paper, we introduce a unified framework for the study of penalty concepts by means of the separation functions in the image space (see Ref. 1). Moreover, we establish new results concerning a correspondence between the solutions of the constrained problem and the limit points of the unconstrained minima. Finally, we analyze some known classes of penalty functions and some known classical results about penalization, and we show that they can be derived from our results directly.     

二阶非线性阻尼微分方程解的振动性质

本文研究了一类二阶非线性阻尼微分方程解的振动性,利用分类讨论和分析的方法,建立了两个新的振动性定理,推广和改进了已有的结果.     

求解不等式约束优化问题的一个改进算法

本文改进了一个求解不等式约束优化问题的对偶算法，建立了一个相应的算法，进一步证明了该算法的收敛性．最后，给出数值结果以验证该算法的有效性。