It is proven that these modified dual algorithms still have the same convergence results as those of the conceptional dual algorithms in chapter 2 and chapter 3 . secondly , a dual algorithm is constructed for general constrained nonlinear programming problems and the local convergence theorem is established accordingly . the condition number of modified lagrange function ' s hessian is estimated , which also depends on the penalty parameter 证明这些修正的对偶算法仍具有同前两章的概念性对偶算法相同的收敛性结果，我们还进一步构造了一般约束非线性规划问题的对偶算法，建立了相应的局部收敛理论，最后估计了修正lagrange函数的hesse阵的条件数，它同样依赖于罚参数。
The general nonlinear programming problem and the basic assumptions under which our convergence results hold are introduced in chapter 2 . in chapter 3 , we give the definition of the mpf which our method is based on , the mpf method and the trust region algorithm . the convergence results for the mpf method , some aspects concerning the practical implementation and some concluded remarks of the method are discussed in chapter 4 第一章为绪论部分，第二章介绍本文收敛性理论所需要的一般非线性规划问题的最优性条件和基本的假设条件，第三章给出修改的罚函数的定义，修改的罚函数法，以及第步迭代所用的信赖域算法，第四章讨论修改的罚函数法的收敛理论，数值实验和由修改的罚函数法得出的一些结论。
Moreover , comparing with simplex method , this algorithm could n ' t cause vibration phenomenon . in section two , issue involves how to cakulate the constrained nonlinear programming problem by sumt and ag . the method overcomes some limitations such as differentiability , continuity or singlepeak of functions etc . its applying category is more extensive than any other existing methods . especially , it is very efficient for us to cakulate huge constrained nonlinear programming problems 第二部分内容是关于如何利用sumt与ag求解带约束条件的非线性规划问题，透过这部分内容，我们将发现，把sumt与ag结合在一起运用到求解带约束条件的非线性规划问题可以克服其他一些算法的局限性，譬如，函数的可导性、单峰性等，因而这种方法的应用范围更广，尤其在求解大型带约束条件的非线性规划问题上效果更为明显。
Zhu has studied unconstrained optimal problem by combining optimal path and modified path with nonmonotonic trust region methods in [ 9 ] , and the use of l2 norm by trust region method in [ 1 ] in seeking the solution of unconstrained optimization has formed simple approximate trust region path , which enlightens us to solve nonlinear programming problem by curvilinear path 朱德通在文[ 9 ]中将最优路径和修正梯度路径与非单调信赖域方法相结合讨论无约束优化问题，且文[ 3 ]中用信赖域方法解无约束优化问题取l _ 2范数形成了形式简单的近似信赖域路径，此类思想启发作者用弧线路径来解决约束优化问题。
In the fourth chapter , several methods for handling constrains by genetic algorithms for nonlinear programming problems are introduced . these methods were grouped into four categories : methods based on preserving feasibility of solutions , methods based on penalty functions , methods which make a clear distinction between feasible and infeasible solutions and other hybrid methods 在第四章中介绍了处理约束的四类方法：算子修正法，罚函数法，可行域搜索法，以及混合遗传算法，并对这些方法做了详细的分析，指出了他们优劣之处。
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 . it makes the initial iterative variable more easy to be determined 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。
