From 223732603380c142d66e3dd08dd906932e16a3b6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=9B=98=E8=8D=A3=E5=8D=9A?= <2858829498@qq.com> Date: Sun, 14 Jul 2024 14:55:42 +0800 Subject: [PATCH] =?UTF-8?q?=E9=9D=9E=E7=BA=BF=E6=80=A7=E8=A7=84=E5=88=92?= =?UTF-8?q?=EF=BC=88P42=E5=BD=A9=E7=94=B5=EF=BC=8C=E6=B1=82=E8=A7=A3?= =?UTF-8?q?=E5=92=8C=E7=81=B5=E6=95=8F=E6=80=A7=E5=88=86=E6=9E=90=EF=BC=89?= =?UTF-8?q?=EF=BC=88=E7=AE=80=E5=8D=95=E7=A4=BA=E4=BE=8B=EF=BC=89=EF=BC=88?= =?UTF-8?q?=E9=80=89=E5=9D=80=E9=97=AE=E9=A2=98=EF=BC=89?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 姚安欣/NLP.m | 135 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 135 insertions(+) create mode 100644 姚安欣/NLP.m diff --git a/姚安欣/NLP.m b/姚安欣/NLP.m new file mode 100644 index 0000000..187a7b8 --- /dev/null +++ b/姚安欣/NLP.m @@ -0,0 +1,135 @@ + +%非线性规划 + +%P42例题 + +%求解 +clc,clear,format long g,close all; +syms x1 x2;%符号变量(用于定义函数、求解方程、计算导数和积分) +f=(339-0.01*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000); +f=simplify(f); +f1=diff(f,x1),f2=diff(f,x2); +[x10,x20]=solve(f1,f2);%求驻点即使f1,f2为0的点 +x10=round(double(x10));%四舍五入 +x20=round(double(x20)); +f0=subs(f,{x1,x2},{x10,x20}); +f0=double(f0); +subplot(121); +fmesh(f,[0,10000,0,10000]);%3维 +%xlabel('x1','Interpreter','latex'); +%ylabel('y1','Interpreter','latex'); +xlabel('x1'); +ylabel('y1'); +subplot(122); +L=fcontour(f,[0,10000,0,10000]); +contour(L.XData,L.YData,L.ZData,'ShowText','on'); +xlabel('x1'); +ylabel('y1'); +p1=339-0.01*x10-0.003*x20; +p2=399-0.004*x10-0.01*x20; +c=195*x10+225*x20+400000; +rate=f0/c; + +%灵敏性检验 分析 最优解 对 19村彩电价格下降幅度 的灵敏性 +clc,clear,close all,format long g; +syms x1 x2 a; +X1=4735,X2=7043,AA=0.01,FF=553641; +f=(339-a*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000); +f1=diff(f,x1),f2=diff(f,x2); +[x10,x20]=solve(f1,f2); + +subplot(121); +fplot(x10,[0.002,0.02]); +xlabel('a'); +ylabel('x1'); + +subplot(122); +fplot(x20,[0.002,0.02]); +xlabel('a'); +ylabel('x2'); + +dx1=diff(x10,a); +dx10=subs(dx1,a,0.01),dx10=double(dx10); +sx1a=dx10*AA/X1; + +dx2=diff(x20,a); +dx20=subs(dx2,a,0.01),dx20=double(dx20); +sx2a=dx20*AA/X2; + +F=subs(f,[x1,x2],[x10,x20]); +F=simplify(F); +figure,fplot(F,[0.002,0.02]); +xlabel('a'); +ylabel('profit'); +dpro=diff(F,a); +dpro0=subs(F,a,0.01); +sya=dpro0*AA/FF; + +%当a提高10% +f3=subs(f,[x1,x2,a],[X1,X2,0.011]),f3=double(f3); +f4=subs(F,[a],0.011); +%相对误差 +delta=(f4-f3)/f4; +delta=double(delta); +%相对误差很小，说明在19寸的价格下降幅度在一定范围内发生变化时，仍然按照不变时的最优解来确定生产方案，仍然可以获得几乎最优的利润。 + + + + + +%使用fmincon的简单例子 + +%蒙特卡罗确定初始值 +clc,clear,close all; +n=10^7; +x1=unifrnd(0,12,[1,n]); +x2=unifrnd(0,12,[1,n]); +fmin=+inf; +for i=1:n + x=[x1(i),x2(i)]; + if ((x1(i)-1)^2-x2(i)-6<=0) & (-2*x1(i)+3*x2(i)-6<=0) + temp=x(1)^2+x(2)^2-x(1)*x(2)-2*x(1)-5*x(2); + if temp