非线性优化

Through a large number of examples in this book describes the basic use of ANSYS 8.1 software methods, including modeling, meshing, applied loads, solving and post-processing, etc.; then introduced using ANSYS finite element analysis process commonly used in high-level analytical methods, such as the non-linear static analysis, modal analysis, transient dynamic analysis, thermodynamic analysis, optimization design, etc.; In addition, the book pairs of ANSYS parametric programming language APDL made an initial set to try to make the reader of this strong preliminary understanding of language.

本书通过大量的实例介绍了ANSYS 8.1软件的基本使用方法，包括建模、网格划分、施加荷载、求解及后处理等；进而介绍了用ANSYS进行有限元分析过程中常用的高级分析方法，如非线性静力分析、模态分析、瞬态动力分析、热力学分析、优化设计等；另外，本书还对ANSYS参数化编程语言APDL作了初步阐述，力图使读者对这种强大的语言有初步的认识。

The simulation results demonstrate this method is valid in parametric optimixation of a nonlinear control system.

仿真结果表明，该方法是一种有效的非线性控制系统参数优化方法。

As we know, perturbed and optimization and varia-tional principle play an important role in nonlinear analysis.

我们知道，扰动优化或变分原理在非线性分析领域中也起到了很大的作用。

The parameter optimization and performance analysis of nonlinear PI controllers of thermal process are studied in this paper.

研究了热力过程非线性PI控制器的参数优化和性能分析问题。

To obtain more practically optimal solutions for production planning in chemical enterprises, piecewise linear function and polynomial function were used to model nonlinear unit consumptions.The optimal solutions obtained by the two approaches were compared in case studies.

为了得到更切合实际的化工企业生产计划优化结果，采用分段线性函数和多项式函数对非线性单耗问题建模并进行比较。

Optimization of planning for drainage system in plain polder area is a complicated multi-dimensional non-linear optimizing problem.

平原圩区除涝排水系统最优规划是一个多维、非线性复杂系统优化问题。

In the computational methods of TPBVP, in order to reduce some difficulties involved in solving a TPBVP via adjoint variables, we discuss a direct method in which state and control variables are indirectly parameterized, The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and control variables, thus converting the optimal control problem into a nonlinear programming problem, which can be solved numerically.

在数值解法中，为了减少解决两点边值问题共轭变量带来的困难，主要讨论了将状态变量和控制变量进行参数化的一种直接方法，这种方法采用了近段发展起来的使用分段的多项式来代替状态和控制变量的直接优化方法，然后最优控制问题就转化成可以用数值方法解决的非线性规划问题，使得迭代初值更加容易选取。

Segmentation and extraction of the target feature points from the unregistered, noisy data set of human body scanning and measuring are discussed. We have fitted the noise scanned data line with KS principal curve, which is based on the K-means theory. The crossing zero of curvature was used to segment and estimate the position of target feature points. And optimization scheme named variable fuzzy partition is also presented to improve the searching for local feature area.

使用基于K-means思想的KS主曲线算法，对国家人体尺寸测量工作中产生的带噪声扫描线数据集合进行非线性拟合，并依据曲率分布特征提出对目标特征点空间位置进行模糊分区估计的方法；同时提出了变量化模糊分区的优化策略，大幅度地提高了局部特征区域搜索的效率。

A general super memory gradient projection method was generalized to solve the nonlinear programming problems about the nonlinear equality constraints and in equality constraints by using general projection matrix.

利用广义投影技术，将求解无约束规划的超记忆梯度算法推广，建立了求解带非线性等式和不等式约束优化问题的一种超记忆梯度广义投影算法，并证明了算法的收敛性。

By using generalized projection matrix, conditions are given on the scalars in the three term-memory gradient direction to ensure that the three term-memory gradient projection direction is a descent direction. A new three term-memory gradient projection method for nonlinear programming with nonlinear equality and in-equality constraints is presented.

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。