非线性规划

This course offers an introduction to primary convex analysis, linear programming, non-linear programming, dynamic programming, multi-objective programming, multi-level programming, calculus of variations, and optimal control, which are the optimization methods commonly used in economics and finance.

课程内容简介：本课程介绍凸分析基础、线性规划、非线性规划、动态规划、多目标规划、多层规划、变分法、最优控制，这些都是西方经济学、金融学中常用的最优化方法。

To inequality constraint s, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

在无约束非线性规划问题全局优化的模拟退火算法基础上，进行有约束问题求解的进一步探讨，对不等式约束条件提出了检验法和罚函数法的处理方法，对等式约束条件开发了罚函数法和解方程法的求解步骤，并进行了分析比较，从而形成了完整的求取非线性规划问题全局优化的模拟退火算法。

According to the optimization design and reactor networks design of chemical system engineering, the method which restriction nonlinear programming problems can be transformed to the no-restriction no-linear programming problems was put forward.

针对化工系统工程中的优化设计、反应器网络设计等问题，提出了一种将有约束的非线性规划问题转化为无约束的非线性规划问题的北京化工大学博士学位论文方法，使用本论文提出的改进遗传算法对这类问题进行了求解，提高了计算效率和计算精度，能有效地寻找到全局最优解。4。

This book discusses linear and nonlinear programming, dynamic programming, integer programming and stochastic programming.

本书讨论了线性和非线性规划，动态规划，整数规划和随机规划。

Multi-model was used in predictive horizon to decrease the predictive error and reflect true state of system.

将非线性系统预测控制的目标函数转化为线性二次规划问题，避免了非线性规划巨大的计算量。

In this paper, an improved algorithm of Wolfe for the constrained nonlinear programming problem is discussed and we offer a new way to research methods of nonlinear programming by that.

中文摘要：本文讨论了约束非线性规划问题的一种Wolfe改进算法，为非线性规划算法的研究提供了一种新途径。

Embedding the gradient direction search and new kinds of evaluation functions into the Genetic Algorithm, a special hybrid Genetic Algorithm with mutation along the weighted gradient direction to solve non-linear programming problems is developed. Then in Chapt 4, a type of nonlinear programming problems with fuzzy objective and fuzzy resources constraints is discussed, in which the objective is ill-defined and the resources possess two different types of fuzzy resources, i. e., tolerance and imprecision. By way of description and formulation of fuzzy objective and fuzzy resources, the problem with fuzzy objective and two different types of fuzzy resources is modelled into a fuzzy nonlinear programming model FO/RNLP and interpreted as three equivalent alternative crisp model to reflect the variety of the environment and the subjective and preference of the decision maker .

本文首先针对遗传算法在求解非线性规划问题中存在的问题，首次提出非可行点／染色体的主导准可行方向，准可行方向，及非可行点属于可行域的可行度等新概念，借助于模糊思想，提出了描述和度量非可行染色体的新方法；通过嵌入非可行染色体的信息于评价函数中，提出了三种新的评价非可行染色体的评价函数；把传统的启发式方法-梯度方向搜索和新的评价函数嵌入到遗传算法中，提出了一种沿加权梯度方向变异的新型混合式遗传算法；第四章针对生产实际中非清晰定义的模糊目标和两种类型的模糊资源，建立了一类连续型模糊目标／资源约束非线性规划问题的模型FO／RNLP。

LINDO for solving linear programming and quadratic programming problems, LINDO LINGO addition to the full functionality, but also can be used for nonlinear programming problem some also can be used for linear and nonlinear equations solution, and so on.

LINDO用于求解线性规划和二次规划问题，LINGO除了具有LINDO的全部功能外，还可以用于求解非线性规划问题，也可以用于一些线性和非线性方程的求解，等等。

Finally, we mainly investigate the following three problems:(1) The problem of portfolio selection with transaction costs is formulated as a bi-objective programming model, but it is no-differentiable and difficult to solve. With a transformation, we can transform the nondifferentiable nonlinear programming problem to a linear program.

然后主要做了如下三个方面的工作：（1）针对带交易费的最优证券组合选择问题可以表示为一类不可微非线性规划模型，但其求解比较困难的特点，提出了一种新的化简方法，一次变换即可将该类不可微非线性规划模型转化为一个线性规划模型，不仅简化了求解过程，而且还减少了最终的线性规划问题的变量个数。

One is a large scale nonlinear programming model with equalities, the other is a more complicated NP hard and nonlinear compound 0-1 programming model. It is difficult for the existed algorithms to fulfill the demands of efficiency and size for the above problems. Two corresponding genetic algorithms are presented, in which several suitable genetic operations are constructed to make the optimization search process in the range of feasible solutions.

一个为大规模的带等式约束的非线性规划模型，另一个为更为复杂的带NP难解问题的混合非线性0-1规划，已有算法都难以满足上述两种问题的求解规模及效率的需要，我们给出了相应的遗传算法，确定了适当的遗传操作，使得问题的寻优过程始终都在可行解范围内进行，不仅提高了优化速度，而且有效地提高了优化效果。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。