starting vector (zero vector) equals lower bounds but gets projected to non-zero vector

1 次查看（过去 30 天）
SA-W
SA-W 2024-10-8
编辑： Bruno Luong 2024-10-11
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 个评论
显示 2更早的评论
Bruno Luong
Bruno Luong 2024-10-10
编辑：Bruno Luong 2024-10-10
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
Bruno Luong 2024-10-11
编辑：Bruno Luong 2024-10-11
Ran in:
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)
Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
sol = 5×1
0 0 0 0 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
opts = optimoptions('fmincon','Algorithm','interior-point');
sol = fmincon(@func, startVec, [], [], [], [], lb, ub, [], opts)
Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
sol = 5×1
1.0e-07 * 0.5003 0.5003 0.5003 0.5003 0.5003
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
function fval = func(x)
fval = sum((x+1).^2);
end

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Walter Roberson
Walter Roberson 2024-10-8
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 个评论
显示 8更早的评论
SA-W
SA-W 2024-10-10
I am happy with what fmincon does. No need to reinvent the wheel.
Just wanted to clarify if the observation I made is the intented behavior of fmincon because it looked odd to me.
@Walter Roberson Maybe you want to rethink your answer?

请先登录，再进行评论。

更多回答（1 个）

Matt J
Matt J 2024-10-10
编辑：Matt J 2024-10-10
Ran in:
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')
Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
sol = 5×1
1.0000 1.0000 1.0000 1.0000 1.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Demo('interior-point')
Error using solution>Demo/func (line 19)
Unexpected values: x is not the zero vector. Current x: 0.99 0.99 0.99 0.99 0.99

Error in objfunEvaluator (line 5)
fval = feval(Objfun, x, self.FunArgs.AdditionalParameters{:});

Error in OptimFunctions/objectiveFirstEval (line 645)
[fval, grad, hess] = self.ObjectiveFunAndGrad(self,self.FunFcn{3},...

Error in fmincon (line 501)
[initVals.f,initVals.g,HESSIAN,funObj] = funObj.objectiveFirstEval(X);

Error in solution>Demo (line 13)
sol = fmincon(@func, startVec, [], [], [], [], lb, ub,[],opts)

Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.
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

类别

在 Help Center 和 File Exchange 中查找有关 Startup and Shutdown 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by