How to find the optimal solution between boundary values?
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If a problem a*x+b/x+c
subjected to 0<x<=d
Condition on a,b,c,d such that for optimal solution 0<x*<d?
For example,
x0=0;
f=@(x)(2*x+5/x+10);
x=fmincon(f,x0,[],[],[],[],0,10)
If plotting this,
If I taking the range, 0 to 10 optimal point is 1.581,that is between the boundary
while in the range of 2 to 4,optimal point is 2,that is in the boundary
Also if the range 4 to 10,optimal point is 4,that is in the boundary
So,my problem is to find out at what condition on a,b,c,d such that solution between the boundary not on boundary.
N.B a,b,c,d values are changable.
2 Comments
Bjorn Gustavsson
on 1 Jun 2022
Start by familiarize yourself with the problem. By that I mean plot the curves (positive x only it seems?) for a range of a, b and c values just to see how the curve varies. That should take you a long way towards solving this problem.
Accepted Answer
Matt J
on 1 Jun 2022
The derivative of the curve is zero at x=sqrt(b/a). So, the condition is,
0<a,
0<b,
sqrt(b/a)<d
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