starting vector (zero vector) equals lower bounds but gets projected to non-zero vector
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I created a small example where I created a start vector euqal to the lower bounds, so the start vector respects the bounds, thought gets projected to non-zero vector when double-checking inside objective function.
Is this a bug or do I miss something here?
n = 5;
lb = zeros(n,1);
ub = Inf(5, 1);
startVec = zeros(n, 1);
sol = fmincon(@(x)func(x), startVec, [], [], [], [], lb, ub);
function fval = func(x)
% start vector (zero vector) becomes [0.99 0.99 0.99 0.99 0.99]
if any(x ~= 0)
error('Unexpected values: x is not the zero vector. Current x: %s', num2str(x'));
end
end
4 件のコメント
Bruno Luong
2024 年 10 月 10 日
編集済み: Bruno Luong
2024 年 10 月 10 日
It does what it does, user should not want to interfer with the optimizer while it is working. Only the final end result it returns count.
Pratically any numerical floating point comparison implementation outthere work with some sort of tolerance, each decides the tolerance to be resonable (based on the estimate scale of your data) in practice. The scale estimation is often empirical, and more like an art than precice math, we just have to accept it.
So far your question does not show anything wrong or bug with FMINCON as far as I can see it.
Bruno Luong
2024 年 10 月 11 日
編集済み: Bruno Luong
2024 年 10 月 11 日
More interesting observation is that the there is always a strict positive tolerance to the constraints on interior point algorithm. Code based on Matt's demo show that in the final solution
n = 5;
lb = zeros(n,1);
ub = Inf(n,1);
startVec = ones(n,1);
opts = optimoptions('fmincon','Algorithm','sqp');
sol = fmincon(@func, startVec, [], [], [], [], lb, ub, [], opts)
opts = optimoptions('fmincon','Algorithm','interior-point');
sol = fmincon(@func, startVec, [], [], [], [], lb, ub, [], opts)
function fval = func(x)
fval = sum((x+1).^2);
end
採用された回答
Walter Roberson
2024 年 10 月 8 日
Although the documentation says that lb specifies that x(i) >= lb(i) for all i the implementing code has
violatedLowerBnds_idx = XOUT(xIndices.finiteLb) <= l(xIndices.finiteLb);
and when true, shifts the bounds away from the starting point.
Notice the <= in the test -- so an input vector that is exactly equal to the lower bounds is considered to be in violation of the bounds.
This is arguably a bug in the implementation.
10 件のコメント
その他の回答 (1 件)
Matt J
2024 年 10 月 10 日
編集済み: Matt J
2024 年 10 月 10 日
This behavior is specific to the interior-point algorithm. As the name suggests, an interior-point algorithm must start at an interior point.
Demo('sqp')
Demo('interior-point')
function Demo(alg)
n = 5;
lb = zeros(n,1);
ub = Inf(5, 1);
startVec = zeros(n, 1);
FirstCall=true;
opts=optimoptions('fmincon','Algorithm',alg);
sol = fmincon(@func, startVec, [], [], [], [], lb, ub,[],opts)
function fval = func(x)
if any(x ~= 0) && FirstCall
error('Unexpected values: x is not the zero vector. Current x: %s', num2str(x'));
else
fval=norm(x-1)^2; FirstCall=false;
end
end
end
2 件のコメント
Bruno Luong
2024 年 10 月 10 日
編集済み: Bruno Luong
2024 年 10 月 11 日
Yes exactly, it's even describeb in the doc where I hightlighted the relevant paragraphe here
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