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%非线性规划
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%P42例题
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%求解
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clc,clear,format long g,close all;
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syms x1 x2;%符号变量(用于定义函数、求解方程、计算导数和积分)
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f=(339-0.01*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000);
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f=simplify(f);
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f1=diff(f,x1),f2=diff(f,x2);
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[x10,x20]=solve(f1,f2);%求驻点即使f1,f2为0的点
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x10=round(double(x10));%四舍五入
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x20=round(double(x20));
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f0=subs(f,{x1,x2},{x10,x20});
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f0=double(f0);
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subplot(121);
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fmesh(f,[0,10000,0,10000]);%3维
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%xlabel('x1','Interpreter','latex');
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%ylabel('y1','Interpreter','latex');
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xlabel('x1');
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ylabel('y1');
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subplot(122);
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L=fcontour(f,[0,10000,0,10000]);
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contour(L.XData,L.YData,L.ZData,'ShowText','on');
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xlabel('x1');
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ylabel('y1');
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p1=339-0.01*x10-0.003*x20;
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p2=399-0.004*x10-0.01*x20;
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c=195*x10+225*x20+400000;
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rate=f0/c;
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%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
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clc,clear,close all,format long g;
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syms x1 x2 a;
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X1=4735,X2=7043,AA=0.01,FF=553641;
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f=(339-a*x1-0.003*x2)*x1+(399-0.004*x1-0.01*x2)*x2-(195*x1+225*x2+400000);
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f1=diff(f,x1),f2=diff(f,x2);
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[x10,x20]=solve(f1,f2);
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subplot(121);
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fplot(x10,[0.002,0.02]);
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xlabel('a');
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ylabel('x1');
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subplot(122);
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fplot(x20,[0.002,0.02]);
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xlabel('a');
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ylabel('x2');
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dx1=diff(x10,a);
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dx10=subs(dx1,a,0.01),dx10=double(dx10);
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sx1a=dx10*AA/X1;
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dx2=diff(x20,a);
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dx20=subs(dx2,a,0.01),dx20=double(dx20);
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sx2a=dx20*AA/X2;
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F=subs(f,[x1,x2],[x10,x20]);
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F=simplify(F);
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figure,fplot(F,[0.002,0.02]);
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xlabel('a');
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ylabel('profit');
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dpro=diff(F,a);
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dpro0=subs(F,a,0.01);
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sya=dpro0*AA/FF;
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%当a提高10%
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f3=subs(f,[x1,x2,a],[X1,X2,0.011]),f3=double(f3);
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f4=subs(F,[a],0.011);
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%相对误差
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delta=(f4-f3)/f4;
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delta=double(delta);
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%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。
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%使用fmincon的简单例子
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%蒙特卡罗确定初始值
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clc,clear,close all;
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n=10^7;
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x1=unifrnd(0,12,[1,n]);
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x2=unifrnd(0,12,[1,n]);
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fmin=+inf;
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for i=1:n
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x=[x1(i),x2(i)];
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if ((x1(i)-1)^2-x2(i)-6<=0) & (-2*x1(i)+3*x2(i)-6<=0)
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temp=x(1)^2+x(2)^2-x(1)*x(2)-2*x(1)-5*x(2);
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if temp<fmin
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fmin=temp;
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x0=x;
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end
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end
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end
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%[x,fval]= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
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A=[-2,3];
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b=6;
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[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1);
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%option=optimoptions('fmincon','Algorithm','sqp');
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%[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1,option);
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disp('Thw optimal solution is:');
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disp(x);
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disp('The minimum value is:');
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disp(fval);
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figure;
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fmesh(@(x1, x2) arrayfun(@(x1, x2) fun1([x1, x2]), x1, x2), [-4, 4, -4, 4]);%用法
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xlabel('x1');
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ylabel('x2');
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zlabel('f(x1,x2)');
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%非线性规划---料场选址
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clc,clear,close all;
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a=[1.25,8.75,0.5,5.75,3,7.25];
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b=[1.25,0.75,4.75,5,6.5,7.25];
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A=[1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0];
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bb=[20;20];
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Aeq=[eye(6),eye(6),zeros(6,4)];
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beq=[3;5;4;7;6;11;];
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lb=[zeros(12,1);-inf;-inf;-inf;-inf];
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x0=[3,5,0,7,0,1,0,0,4,0,6,10,5,1,2,7];
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[xans,fvans]=fmincon(@fun2,x0,A,bb,Aeq,beq,lb,[]);
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