多体动力学优化的并行SQP方法

并行计算的发展大大提高计算机的计算效率,降低计算时间.针对多体动力学的优化问题,分析了求解灵敏度的三种方法的并行性,建立了有限差分法与直接微分法的并行算法.同时采用并行Armijo线性搜索,构成了完整的并行序列二次规划(SQP)算法.将上述算法应用到曲柄滑块的优化中,并与串行SQP算法进行了比较,证实了并行SQP算法可以大大降低计算时间.上述研究为多体动力学优化提供了一种并行求解思路.     

A new SQP approach for nonlinear complementarity problems

Sequential quadratic programming (SQP) methods have been extensively studied to handle nonlinear programming problems. In this paper, a new SQP approach is employed to tackle nonlinear complementarity problems (NCPs). At each iterate, NCP conditions are divided into two parts. The inequalities and equations in NCP conditions, which are violated in the current iterate, are treated as the objective function, and the others act as constraints, which avoids finding a feasible initial point and feasible iterate points. NCP conditions are consequently transformed into a feasible nonlinear programming subproblem at each step. New SQP techniques are therefore successful in handling NCPs.     

基于N-S方程和序列二次规划的翼型优化设计

实际工程中的翼型设计通常是对某一性能良好的基本翼型进行局部改进以满足特定的工程要求。中将N—S方程流场分析程序和序列二次规划结合起来，发展了一种实用的翼型优化设计方法，用以提高基本翼型在多个设计点、在多种约束条件下的气动性能。由N—S方程计算得到的升力、阻力等气动参数构成目标函数，数值优化程序对其进行最优化。超临界翼型的设计算例表明，中发展的翼型优化方法设计质量高，所需机时少，易于实施，有较大的工程应用价值。     

涡轴发动机最优加速控制研究

研究了航空涡轴发动机加速过程的最优控制问题。采用的优化方法是序列二次规划法(SQP)。研究表明，将序列二次规划法应用于涡轴发动机最优加速控制是可行的，加速过程的寻优控制规律正确。在8项约束的范围内以及在保证发动机安全的前提下，与传统的PID控制结果相比，改善了发动机的动态性能，达到进一步发挥发动机性能潜力的目的。     

A globally convergent trust region multidimensional filter SQP algorithm for nonlinear programming

We propose a trust region multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 15 (2005), pp. 17–38] is extended to solve constrained optimization problems. The constraints are partitioned into p parts. The entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but also the individual behaviour of each part of the constraints is considered. The filter's entries and the acceptance criteria are different from other filter-related algorithms in the literature. It should be noted that the undesirable link between the objective function and the constraint violation function in the filter acceptance criteria disappears. Our algorithm is also combined with the non-monotone technique for accepting a trial step, which leads to a more flexible acceptance criteria. Under mild conditions, global convergence is proved. Numerical results show the robustness and efficiency of our algorithm.     

乙烯脱丁烷塔智能操作优化方法研究

考虑乙烯生产过程中实时操作优化特点,在建立精馏塔严格机理开放式方程优化模型的基础上,提出了基于简约空间序列二次规划(RSQP)算法的精馏塔智能操作优化方法.该法根据精馏塔优化操作的实际性和实时性要求,对简约空间SQP算法进行了一些特殊处理,对收敛条件加入了一些智能化规则,使得优化算法综合考虑优化效益、优化求解时间和质量约束等方面.计算结果表明该法的计算效率高于基于Snopt和一般简约空间SQP算法的精馏塔操作优化方法,并且该方法更符合实时操作优化的要求.     

基于有限元方法的碾压混凝土重力坝坝体体型优化研究

采用非线性优化方法中的序列二次规划法（SQP）优化碾压混凝土重力坝坝体体型。此方法以坝体混凝土总造价为目标函数，采用弹塑性有限元方法计算坝体的应力，并且在“准弹性稳定法则”的基础上提出了有限元计算碾压混凝土重力坝应力的控制标准。该方法不仅考虑了坝体材料分区问题而且在优化过程中考虑了河谷形状对目标函数的影响，采用更多变量的组合，进行坝体体型优化设计。计算实例表明，在满足设计安全的前提下，能获得经济、实用的坝体体型。     

The Direct Solution of Nonconvex Nonlinear FIR Filter Design Problems by a SIP Method

FIR filter design problems in the frequency domain are nonlinear (semi-infinite) optimization problems. In practice, however, these almost always have not been approached directly, but been solved in a simplified form and/or only under restricting assumptions. In this paper, quite general mathematical formulations of the four main design approximation problems in the frequency domain are presented, which enable the derivation of theoretical results (collected here from R. Reemtsen, 2000b, 2000c) and the application of general-purpose optimization procedures to their direct solution. For the actual solution, a nonlinear semi-infinite programming method from the thesis (S. Görner, Ph.D. Thesis, Technische Universität Berlin, Berlin, 1997) of the first author is discussed and applied to several specific design problems. In some cases, the computed solution of the nonlinear problem is compared with that of a convex approximation of the problem.     

水下隔声材料的声学优化设计

将约束优化理论引入声学设计领域,以带结构的水下隔声层为分析对象,阐述了序列二次规划算法用于声学优化设计的基本过程和关键步骤。通过对带结构的水下隔声层所用橡胶材料参数的优化设计,为水下隔声橡胶的参数设计提供了设计的基本方向,对于提高其水下隔声性能具有重要意义。     

Optimization of large‐scale truss structures using sparse SAND formulations

Sparsity features of simultaneous analysis and design (SAND) formulations are studied and exploited for optimization of large‐scale truss structures. Three formulations are described and implemented with an existing analysis code. SAND formulations have large number of variables; however, gradients of the functions and Hessian of the Lagrangian are quite sparsely populated. Therefore, this structure of the problem is exploited and an optimization algorithm with sparse matrix capability is used to solve large‐scale problems. An existing analysis software is integrated with an optimizer based on a sparse sequential quadratic programming (SQP) algorithm to solve sample problems. The formulations and algorithms work quite well for the sample problems, and their performances are compared and discussed. For all the cases considered, the SAND formulations out perform the conventional formulation except one case. Further research is suggested to fully study and utilize sparse features of the alternative SAND formulations and to develop more efficient sparse solvers for large‐scale and more complex applications. Copyright © 2006 John Wiley & Sons, Ltd.