[问答] 请教如何用Matlab求解一个约束优化问题 [推广有奖]

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T-back 发表于 2011-4-11 19:53:42 |AI写论文

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min f(x1,x2,x3)=x1^2+x2^2+x3^2+x1*x2+x1*x3+x2*x3
s.t.: x1+x2+x3=1 , x1>=0,x2>=0,x3>=0
请问各位，此约束问题如何用Matlab编程实现，谢谢帮助!

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qibbxxt 发表于 2011-4-12 11:04:46

>> f=@(x1,x2,x3)x1.^2+x2.^2+x3.^2+x1.*x2+x1.*x3+x2.*x3;
>> Aeq =[1,1,1];beq = 1;
>> x = fmincon(@(x)f(x(1),x(2),x(3)),[0.4,0.3,0.3],[],[],Aeq,beq,[0 0 0 ],[])
Warning: Trust-region-reflective algorithm does not solve this type of problem, using active-set
algorithm. You could also try the interior-point or sqp algorithms: set the Algorithm option to
'interior-point' or 'sqp' and rerun. For more help, see Choosing the Algorithm in the documentation.
> In fmincon at 472
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints were satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
No active inequalities.
x =
0.3333 0.3333 0.3333