挤出平缝口模优化设计

挤出平缝口模通常用于加工膜和片材，对产品厚度的一致性有很高要求。本文给出了结合聚合物成型模拟技术、设计灵敏度分析和数值优化技术的口模形状优化设计方法。以最小压力降为目标函数，口模出口处任意点的速率与出口已知速率相对误差的平方和小于容许误差为约束函数，口模形状参数为优化设计变量，给出了目标函数的表达式，推导了日标函数、约束函数对优化设计变量的灵敏度公式。利用灵敏度分析和基于梯度的优化算法即序列二次规划算法(SQP法)求解最优设计参数。通过算例表明，应用该法进行口模优化设计可以减小压力降和口模出口速率变化率。     

解非线性规划问题的不精确线性搜索SQP滤子方法

本文用序列二次规划方法(SQP)结合Wolfe-Powell不精确线性搜索准则求解非线性规划问题.Wolfe-Powell准则是一种能够使目标函数获得充分下降而运行时间较省的确定步长方法.不精确线性搜索滤子方法比较其它结合精确线性搜索和信赖域方法求解问题的滤子方法更灵活更易实现.如果目标函数的预测下降量为负,我们的工作将主要利用可行恢复项改善可行性.一般条件下,本文提出的算法较易实现,且具有全局收敛性.数值试验显示了算法的有效性.     

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

In a composite-step approach, a step sk is computed as the sum of two components vk and hk. The normal component vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, sk is a compositestep composed of normal component Vk and tangential component hk.     

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.     

一种新的结合NCP函数的SQP滤子算法

对于SQP滤子算法,本文提出了一种新方法来构造滤子,目的是为了使滤子的接受条件更宽松,降低进行可行性恢复的机率.另外,本文通过一些数值例子对这种新算法进行了检验,事实证明这种算法是有效的.最后还证明这种算法具有超线性收敛性.     

约束优化的一个改进的强次可行SQP算法及数值试验

本文对约束优化一个强次可行SQP算法进行改进,使之产生的迭代点在有限次迭代后全落入可行域;并对算法数值效果进行了大量的比较试验.     

Parameter estimation of ordinary differential equations

This paper addresses the development of a new algorithm forparameter estimation of ordinary differential equations. Here,we show that (1) the simultaneous approach combined with orthogonalcyclic reduction can be used to reduce the estimation problemto an optimization problem subject to a fixed number of equalityconstraints without the need for structural information to devisea stable embedding in the case of non-trivial dichotomy and(2) the Newton approximation of the Hessian information of theLagrangian function of the estimation problem should be usedin cases where hypothesized models are incorrect or only a limitedamount of sample data is available. A new algorithm is proposedwhich includes the use of the sequential quadratic programming(SQP) Gauss–Newton approximation but also encompassesthe SQP Newton approximation along with tests of when to usethis approximation. This composite approach relaxes the restrictionson the SQP Gauss–Newton approximation that the hypothesizedmodel should be correct and the sample data set large enough.This new algorithm has been tested on two standard problems.     

非线性最优化一个可行序列等式约束二次规划算法

本文针对非线性不等式约束优化问题,提出了一个新的可行序列等式约束二次规划算法．在每次迭代中,该算法只需求解三个相同规模且仅含等式约束的二次规划(必要时求解一个辅助的线性规划),因而其计算工作量较小．在一般的条件下,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

General Information

In this paper, we propose and analyze an SQP-type method for solving linearly constrained convex minimization problems where the objective functions are too complex to be evaluated exactly. Some basic results for global convergence and local superlinear convergence are obtained according to the properties of the approximation sequence. We illustrate the applicability of our approach by proposing a new method for solving two-stage stochastic programs with fixed recourse.     

SQP algorithms for solving Toeplitz matrix approximation problem

Given an n × n matrix F, we find the nearest symmetric positive semi‐definite Toeplitz matrix T to F. The problem is formulated as a non‐linear minimization problem with positive semi‐definite Toeplitz matrix as constraints. Then a computational framework is given. An algorithm with rapid convergence is obtained by l₁ Sequential Quadratic Programming (SQP) method. Copyright © 2002 John Wiley & Sons, Ltd.