MATLAB学习（七）求解优化问题：线性规划 非线性规划 拟合与插值 多目标规划

Minf(x)=-5x1  -4x2  -6x3

               x1   -x2    +x3  <=20

             3x1  +2x2 +4x3 <=42

               3x1 +2x2           <=30

            0<=x1,0<=x2,0<=x3

>> c=[-5,-4,-6];
>> A=[1 -1 1
3 2 4
3 2 0];
>> b=[20;42;30];
>> lb=zeros(3,1);
>> [x,fval,exitflag,output,lambda]=linprog(c,A,b,[],[],lb)
Optimization terminated.
x =
    0.0000
   15.0000
    3.0000
fval =
  -78.0000
exitflag =
     1
output = 
         iterations: 6
          algorithm: 'interior-point-legacy'
       cgiterations: 0
            message: 'Optimization terminated.'
    constrviolation: 0
      firstorderopt: 5.8705e-10
lambda = 
    ineqlin: [3x1 double]
      eqlin: [0x1 double]
      upper: [3x1 double]
      lower: [3x1 double]
>>

function[c,ceq]=mycon(x)
c1=1.5+x(1)*x(2)-x(1)-x(2);
c2=-x(1)*x(2)-10;
c=[c1;c2];       % 非线性不等式约束
ceq = [];        % 非线性等式约束

　　

>> optf=@(x) exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1);
>> x0=[10;10];lb=[0;0];ub=[inf;inf];
>> options=optimset('Algorithm','active-set','Display','off');
>> [x,fval] = fmincon(optf,x0,[],[],[],[],lb,ub,@mycon,options)
x =
         0
    1.5000
fval =
    8.5000
>>

　　

>> x=0:.1:5;
>> y=sin(x);
>> f=@(b,x)  b(1)*cos(b(2)*x+b(3))+b(4);
>> [a,ss]=lsqcurvefit(f,[1,1,1,1],x,y)
Local minimum found.
Optimization completed because the size of the gradient is less than
the default value of the function tolerance.
<stopping criteria details>
a =
   -1.0000    1.0000    1.5708   -0.0000
ss =
   8.7594e-29
>> xf=0:0.05:8;
yfit=f(a,xf);
plot(xf,sin(xf),'ro',xf,yfit,'b-')

　　

>> zf=@(a,x) a(1)*x(:,1).^2+a(2)*x(:,2).^2+a(3) %构造拟合函数类型
zf = 
    @(a,x)a(1)*x(:,1).^2+a(2)*x(:,2).^2+a(3)
>> [X0,Y0]=meshgrid(-2:.2:2);
x0=X0(:);y0=Y0(:);
z0=zf([1,1,-1],[x0,y0]);
>> %用上面的点去拟合估计曲面函数中的参数a:
>> [b,re]=nlinfit([x0,y0],z0,zf,[0,0,0]);
b %显示b，发现恰好是1、1、-1
b =
    1.0000    1.0000   -1.0000

　　

 

>> [X,Y] = meshgrid(-3:.25:3);Z = peaks(X,Y);
[XI,YI] = meshgrid(-3:.125:3);
ZI = interp2(X,Y,Z,XI,YI);
mesh(X,Y,Z), hold, mesh(XI,YI,ZI+15), hold off
axis([-3 3 -3 3 -5 20])
已锁定最新绘图
>>