代數(shù)方程與最優(yōu)化問(wèn)題的計(jì)算機(jī)求解課件

1、第 6 章代數(shù)方程與最優(yōu)化問(wèn)題的計(jì)算機(jī)求解薛定宇、陳陽(yáng)泉著高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解，清華大學(xué)出版社2004CAI課件開(kāi)發(fā)：劉瑩瑩、薛定宇2022/7/241高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解主要內(nèi)容代數(shù)方程的求解無(wú)約束最優(yōu)化問(wèn)題求解有約束最優(yōu)化問(wèn)題的計(jì)算機(jī)求解整數(shù)規(guī)劃問(wèn)題的計(jì)算機(jī)求解2022/7/242高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.1 代數(shù)方程的求解代數(shù)方程的圖解法多項(xiàng)式型方程的準(zhǔn)解析解法一般非線性方程數(shù)值解2022/7/243高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.1.1 代數(shù)方程的圖解法6.1.1.1 一元方程的圖解法【例6-1】2022/7/244高等應(yīng)用數(shù)學(xué)問(wèn)題的MAT

2、LAB求解6.1.1.2 二元方程的圖解法【例6-2】2022/7/245高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.1.2 多項(xiàng)式型方程的準(zhǔn)解析解法【例6-3】2022/7/246高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/247高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-4】2022/7/248高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-5】2022/7/249高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2410高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-6】2022/7/2411高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-7】2022/7/2412高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.1.3

3、一般非線性方程數(shù)值解2022/7/2413高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2414高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-8】2022/7/2415高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-9】2022/7/2416高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2417高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-10】2022/7/2418高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2419高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.2 無(wú)約束最優(yōu)化問(wèn)題求解解析解法和圖解法基于MATLAB的數(shù)值解法全局最優(yōu)解與局部最優(yōu)解利用梯度求解最優(yōu)化問(wèn)題2022/7/2420高等應(yīng)用數(shù)學(xué)問(wèn)

4、題的MATLAB求解6.2.1 解析解法和圖解法2022/7/2421高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-11】2022/7/2422高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2423高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.2.2 基于 MATLAB 的數(shù)值解法2022/7/2424高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-12】2022/7/2425高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2426高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2427高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.2.3 全局最優(yōu)解與局部最優(yōu)解【例6-13】2022/7/2428高等應(yīng)用數(shù)學(xué)問(wèn)題的M

5、ATLAB求解2022/7/2429高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.2.4 利用梯度求解最優(yōu)化問(wèn)題【例6-14】2022/7/2430高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2431高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2432高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.3 有約束最優(yōu)化問(wèn)題的計(jì)算機(jī)求解約束條件與可行解區(qū)域線性規(guī)劃問(wèn)題的計(jì)算機(jī)求解二次型規(guī)劃的求解一般非線性規(guī)劃問(wèn)題的求解2022/7/2433高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.3.1 約束條件與可行解區(qū)域2022/7/2434高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-15】2022/7/2435高等應(yīng)用數(shù)學(xué)問(wèn)

6、題的MATLAB求解6.3.2 線性規(guī)劃問(wèn)題的計(jì)算機(jī)求解2022/7/2436高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-16】2022/7/2437高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-17】2022/7/2438高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.3.3 二次型規(guī)劃的求解2022/7/2439高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-18】2022/7/2440高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.3.4 一般非線性規(guī)劃問(wèn)題的求解2022/7/2441高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-19】2022/7/2442高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2443高等應(yīng)用數(shù)

7、學(xué)問(wèn)題的MATLAB求解2022/7/2444高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-20】2022/7/2445高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2446高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2447高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.4 整數(shù)規(guī)劃問(wèn)題的計(jì)算機(jī)求解整數(shù)線性規(guī)劃問(wèn)題的求解一般非線性整數(shù)規(guī)劃問(wèn)題與求解0-1規(guī)劃問(wèn)題求解2022/7/2448高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.4.1 整數(shù)線性規(guī)劃問(wèn)題的求解免費(fèi)工具箱，可以由MathWorks公司網(wǎng)站下載，也可以由本書(shū)光盤得出2022/7/2449高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-21】2022

8、/7/2450高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2451高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2452高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.4.2 一般非線性整數(shù)規(guī)劃問(wèn)題與求解2022/7/2453高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-22】2022/7/2454高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2455高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-23】2022/7/2456高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2457高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2458高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解6.4.3 0-1規(guī)劃問(wèn)題求解MAT

9、LAB 7.0 版本提供的 0-1 線性規(guī)劃問(wèn)題當(dāng)然也可以用前面的函數(shù)求解2022/7/2459高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-24】2022/7/2460高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解2022/7/2461高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解【例6-25】2022/7/2462高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解本章內(nèi)容簡(jiǎn)介2022/7/2463高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解數(shù)學(xué)方程求解是科學(xué)與工程研究中經(jīng)常遇到的問(wèn)題，本章先介紹了簡(jiǎn)單方程的圖解法，給出了方程求解的基本概念，并介紹了基于符號(hào)運(yùn)算工具箱中 solve( ) 函數(shù)的多項(xiàng)式類方程的準(zhǔn)解析求解算法，還介紹了基于最優(yōu)化工

10、具箱 fsolve( ) 函數(shù)求取一般非線性方程的數(shù)值解法。2022/7/2464高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解本章介紹了無(wú)約束最優(yōu)化問(wèn)題及 MATLAB 解決方案，并引入了全局最優(yōu)解與局部最優(yōu)解的概念。本章還介紹了若干種有約束最優(yōu)化問(wèn)題，介紹了可行解區(qū)域的概念，并介紹了最優(yōu)化問(wèn)題求解算法的 MATLAB 求解方法，如線性規(guī)劃問(wèn)題、二次型規(guī)劃問(wèn)題及一般非線性規(guī)劃問(wèn)題，用這樣的方法可以輕易求解出較復(fù)雜的非線性規(guī)劃問(wèn)題。2022/7/2465高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB求解本章中系統(tǒng)介紹了整數(shù)規(guī)劃問(wèn)題的計(jì)算機(jī)求解方法，引入了整數(shù)線性規(guī)劃問(wèn)題求解工具箱、一般非線性整數(shù)規(guī)劃問(wèn)題求解函數(shù) bnb20( )。由 MATLAB 7.0 版本中給出的新函數(shù)bintprog( ) 探討了 0-1 整數(shù)線性規(guī)劃問(wèn)題的計(jì)算機(jī)求解。借助分枝定界法的 bnb20( ) 函數(shù)還可以求解 0-1 非線性規(guī)劃問(wèn)題。2022/7/2466高等應(yīng)用數(shù)學(xué)問(wèn)題的MATLAB