线性最优化问题

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

In chapter 4 we proposed a linear inequality constraint optimization question frame about projection of gradient algorithm, and has performed the numerical experimentation, but its convergence also needs further study.

在第四章中我们提出了线性不等式约束最优化问题的一个投影梯度算法框架，做了数值试验，但其收敛性还有待进一步研究。

The third chapter constructs a derivative-free optimization method for linear equality constrained optimization problem and gives the proofs of the global convergence.

第三章提出了线性等式约束最优化问题的非单调无导数优化算法，并证明了这种算法的全局收敛性。

COURSE TOPICS : This course is intended to provide a thorough background of computational methods for the solution of linear and nonlinear optimization problems.

本课程讲授完全的关于线性和非线性最优化问题的计算解法的背景知识。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

In Chapter 2, combining two types of the preconvex part of modified Broydens family with Armijo line search, we get two algorithms for solving unconstrained optimization problems, and prove these algorithms are global and superlinear convergence under some suitable conditions.

第二章，将两种修改Broyden非凸族与Armijo线搜索相结合，得到了求解无约束最优化问题两种算法，在适当的条件下，证明了这些算法具有全局收敛性和超线性收敛性。

In Chapter 3, we propose two new quasi-Newton type trust region methods for solving unconstrained optimization problems. These algorithms combine two types of the preconvex part of modified Broydens family proposed in chapter 1 with trust region algorithm effectively, they have global convergence property and superlinear convergence rate.

第三章，给出了用来求解无约束最优化问题两种新的拟牛顿信赖域算法，这些算法将第一章给出的两种修改Broyden非凸族与信赖域算法有效结合起来，它们具有全局收敛性和超线性收敛速度。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。