%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<fmin
           fmin=temp;
           x0=x;
        end
    end
end

%[x,fval]= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

A=[-2,3];
b=6;
[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1);

%option=optimoptions('fmincon','Algorithm','sqp');
%[x,fval]=fmincon(@fun1,x0,A,b,[],[],[],[],@nonlfun1,option);

disp('Thw optimal solution is:');
disp(x);                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
disp('The minimum value is:');
disp(fval);
figure;
fmesh(@(x1, x2) arrayfun(@(x1, x2) fun1([x1, x2]), x1, x2), [-4, 4, -4, 4]);%用法

xlabel('x1');
ylabel('x2');
zlabel('f(x1,x2)');


%非线性规划---料场选址
clc,clear,close all;
a=[1.25,8.75,0.5,5.75,3,7.25];
b=[1.25,0.75,4.75,5,6.5,7.25];
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];
bb=[20;20];
Aeq=[eye(6),eye(6),zeros(6,4)];
beq=[3;5;4;7;6;11;];
lb=[zeros(12,1);-inf;-inf;-inf;-inf];
x0=[3,5,0,7,0,1,0,0,4,0,6,10,5,1,2,7];
[xans,fvans]=fmincon(@fun2,x0,A,bb,Aeq,beq,lb,[]);