Stability analysis for stochastic programs

For stochastic programs with recourse and with (several joint) probabilistic constraints, respectively, we derive quantitative continuity properties of the relevant expectation functionals and constraint set mappings. This leads to qualitative and quantitative stability results for optimal values and optimal solutions with respect to perturbations of the underlying probability distributions. Earlier stability results for stochastic programs with recourse and for those with probabilistic constraints are refined and extended, respectively. Emphasis is placed on equipping sets of probability measures with metrics that one can handle in specific situations. To illustrate the general stability results we present possible consequences when estimating the original probability measure via empirical ones.     

The design of branch and bound algorithms for a class of nonlinear integer programs

This paper is concerned with computational experimentation leading to the design of effective branch and bound algorithms for an important class of nonlinear integer programming problems, namely linearly constrained problems, which are used to model several real-world situations. The main contribution here is a study of the effect of node and branching variable selection and storage reduction strategies on overall computational effort for this class of problems, as well as the generation of a set of adequate test problems. Several node and branching variable strategies are compared in the context of a pure breadth-first enumeration, as well as in a special breadth and depth enumeration combination approach presented herein. Also, the effect of using updated pseudocosts is briefly addressed. Computational experience is presented on a set of eighteen suitably-sized nonlinear test problems, as well as on some random linear integer programs. Some of the new rules proposed are demonstrated to be significantly superior to previously suggested strategies; interestingly, even for linear integer programming problems.     

Post-optimality sensitivity analysis in abstract spaces with applications to continuous-time programming problems

The programming problem under consideration consists in maximizing a concave objective functional, subject to convex operator inequality contraints. The assumptions include the existence of an optimum solution, Fréchet differentiability of all operators involved, and the existence of the topological complement of the null space of the Fréchet derivative of the constraint operator. It is shown that the rate of change of the optimum value of the objective functional due to the perturbation is measured by the dual. The optimum values of the primal variables are locally approximated as linear functions of the perturbation; the theory of generalized inverse operators is used in the approximation. We give an approximation to the primal variables if the problem is perturbed. The results are specialized for some continuous-time and finite-dimensional cases. Two examples for finite-dimensional problems are given. We apply the theory to the continuous-time linear programming problem and prove some continuity results for the optimal primal and dual objective functionals.The authors are indebted to the Natural Sciences and Engineering Research Council of Canada for financial support through Grants A4109 and A7329, respectively. They would also like to thank the referee for his comments.     

A comparison between a primal and a dual cutting plane algorithm for posynomial geometric programming problems

In this paper, primal and dual cutting plane algorithms for the solution of posynomial geometric programming problems are presented. It is shown that these cuts are deepest, in the sense that they cut off as much of the infeasible set as possible. Problems of nondifferentiability in the dual cutting plane are circumvented by the use of a subgradient. Although the resulting dual problem seems easier to solve, the computational experience seems to show that the primal cutting plane outperforms the dual.     

Ergodicity and symmetric mathematical programs

The paper provides new conditions ensuring the optimality of a symmetric feasible point of certain mathematical programs. It is shown that these conditions generalize and unify most of the known results dealing with optimality of symmetric policies (e.g. [2, 4, 6, 11]). The generalization is based on certain ergodic properties of nonnegative matrices. An application to a socio-economic model dealing with optimization of a welfare function is presented.     

A Polyhedral Approach for Nonconvex Quadratic Programming Problems with Box Constraints

We apply a linearization technique for nonconvex quadratic problems with box constraints. We show that cutting plane algorithms can be designed to solve the equivalent problems which minimize a linear function over a convex region. We propose several classes of valid inequalities of the convex region which are closely related to the Boolean quadric polytope. We also describe heuristic procedures for generating cutting planes. Results of preliminary computational experiments show that our inequalities generate a polytope which is a fairly tight approximation of the convex region.     

High-performance networks for broadband multimedia services

Research and development in Advanced Communications technologies for Europe (RACE) played a key role in developing the crucial technology of Asynchronous Transfer Mode (ATM), which can provide a high-performance networking platform for broadband multimedia communications while allowing access to the existing worlds of voice, data, and broadcasting. The functionalities of high-performance networks in the user plane, control plane, and management planes to provide integral performance for the satisfaction of the users have been tested in accompanying measures such as the TEN-IBC projects of the European Commission. The European Union (EU) is now starting Advanced Communications Technologies and Services (ACTS)—the follow-up to RACE—as one of the major specific programs in the fourth research framework, involving 630 million ECUs of European Union contribution over four years. High-performance networking is a key development area within ACTS. It has a clear objective of enabling the deployment of a coherent and comprehensive trans-European information highway consisting of a terrestrial (optical), mobile, and satellite network infrastructure supporting broadband multimedia communications with maximum flexibility and a cost-effective evolution approach. Operational trials of high-performance networks involving different types of users, applications, network operators (national hosts), and the European ATM pilot network are planned as a part of the new ACTS projects. This article summarizes the projects involved and their activities toward the objectives of provisioning the high-performance network information highway for broadband multimedia applications.     

Linearly convergent descent methods for the unconstrained minimization of convex quadratic splines

We propose two linearly convergent descent methods for finding a minimizer of a convex quadratic spline and establish global error estimates for the iterates. One application of such descent methods is to solve convex quadratic programs, since they can be reformulated as problems of unconstrained minimization of convex quadratic splines. In particular, we derive several new linearly convergent algorthms for solving convex quadratic programs. These algorithms could be classified as row-action methods, matrix-splitting methods, and Newton-type methods.     

Unconstrained convex programming approach to linear programming

Recently, Fang proposed approximating a linear program in the Karmarkar standard form by adding an entropic barrier function to the objective function and derived an unconstrained dual concave program. We present in this note a necessary and sufficient condition for the existence of a dual optimal solution to the perturbed problem. In addition, a sharp upper bound of error estimation in this approximation scheme is provided.     

生长曲线分析中的多水平模型及算法

生长曲线分析是了解事物随时间的变化特点的分析热点.然而,传统的曲线拟合方法不适用通过重复测量得到的结构资料.采用轮廓设计矩阵运算虽然解决结构资料的生长曲线分析,但是相应的SAS程序冗长且难懂.将多水平模型应用于生长曲线的分析,通过实例分析介绍应用过程,同时给出简单明了的SAS程序.