Need help for solving an Optimization problem with Nonlinear constraints
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Does someone can help me for the problem below, any answer will be appreciated.
whether the function 'fmincon' or other function in matlab can solve the following problem:
% N
% minimize ∑ {C(i)*V(i)} % objective function
% i=1
% subject to:
% -1 ≤ V(i) ≤ 1;
% 0 ≤ Y(i) ≤ 1;
% 0.6 ≤ Y(N) ≤ 1;
% Y(i+1)-Y(i)=(1-Y(i))*V(i)/20;
%
given Y0=0.3; N=30; vector C is given;
while N is small, like 3 or 4, I can represent Y(3) with Y0,V(1),V(2),V(3). However, when N is big, it's hard to formulate the constrained function.
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回答（1 个）
Alan Weiss
2012-8-6
编辑：Alan Weiss
2012-8-6
It seems to me that your Y vector is a deterministic function of your V vector, and that you minimize over a set of V vectors.
If this is corrrect, you should write a function that gives Y as a function of V, and then write your Y constraints as a set of nonlinear inequalities, and give the V constraints as bounds. Something like the following
function Yout = Ycalc(V)
Yout = zeros(size(V));
Yout(1) = .3 + .7*V(1)/20;
for ii = 2:length(V)
Yout(ii) = Yout(ii-1) + (1-Yout(ii-1))*V(ii)/20;
end
Now that you have this function, write the nonlinear constraints:
-Y(ii)
Y(ii) - 1
Alan Weiss
MATLAB mathematical toolbox documentation
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