Global Convergence of a Nonlinear Programming Method Using Convex Approximations

The method of moving asymptotes (MMA) and its globally convergent extension SCP (sequential convex programming) are known to work well for certain problems arising in structural optimization. In this paper, the methods are extended for a general mathematical programming framework and a new scheme to update certain penalty parameters is defined, which leads to a considerable improvement in the performance. Properties of the approximation functions are outlined in detail. All convergence results of the traditional methods are preserved.     

面向对象设计(OOP)在CIMS中的应用初探

本文简要介绍了OOP技术的基本概念和原理，并结合CIMS系统的特点，介绍了利用OOP支撑软件开发CIMS系统的方法。     

The apolar bilinear form in geometric modeling

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

     

Optimality for (<Emphasis Type="Italic">h,φ</Emphasis>)-multiobjective programming involving generalized type-I functions

Based upon Ben-Tal’s generalized algebraic operations, new classes of functions, namely (h,φ)-type-I, quasi (h,φ)-type-I, and pseudo (h,φ)-type-I, are defined for a multi-objective programming problem. Sufficient optimality conditions are obtained for a feasible solution to be a Pareto efficient solution for this problem. Some duality results are established by utilizing the above defined classes of functions, considering the concept of a Pareto efficient solution. This research is supported by National Science Foundation of China under Grant No. 69972036.     

热压机框板结构优化设计

本文采用有限单元法和数学规划法相结合的“部分线性化结构优化方法”对热压机框板进行重量最轻结构优化设计,在保证满足各项性能指标的前提下,有效地减轻了框极重量,具有明显的经济效益。     

基于知识的成卷方法及在MATBAS系统中的实现

本文以 MATBAS(高等数学试题库及计算机辅助命题和评估软件系统)为背号,论述了基于知识的成卷方法。在分析各类考试特点与规律的基础上,提出三类考试模型。在成卷推理中综合使用可信度推理、启发式推理、规划及约束方法。为了使系统控制更灵活,能够生成若干风格不同的等价试卷,还提出了知识层次划分的思想,引入“元知识”的概念,把知识处理结构设计为耦合式的知识库系统。该成卷方法不仅适用于高等数学命题,也适应于别的课程考试。     

An exponential example for Terlaky's pivoting rule for the criss-cross simplex method

Recently T. Terlaky has proposed a new pivoting rule for the criss-cross simplex method for linear programming and he proved that his rule is convergent. In this note we show that the required number of iterations may be exponential in the number of variables and constraints of the problem.     

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.     

On differential stability in stochastic programming

In this paper optimal solutions of a stochastic programming problem are considered as functions of the underlying probability distribution. Their directional derivatives, in the sense of Gâteaux, are calculated by applying some recent results from the sensitivity analysis of nonlinear programs. These derivatives are employed as a heuristic device in order to derive the asymptotic distribution of statistical estimators of the optimal solutions.