MATLAB: Hello there, I need to solve optimization problem.

fminconfminimax

Hello, I have two interconnected functions z and t where x:
x=176^a-0.0003^(1-a);
z=x*0.016; 0<z<0.2;
t=x*0.0005; 0<t<800;
I need to find optimal a, which is constrained 0.5<a<0.75 to maximize z and t at the same time. What solution would you suggest?

Best Answer

You really only have one function.
z = x*0.016, 0 < z < 0.2
is the same as
0 < x < 0.2/0.016
and
t=x*0.0005; 0<t<800;
is the same as
0 < x < 800/0.0005
The first of those is 0 < x < 12.5, and the second is 0 < x < 1600000, so the first one of those dominates.
You have
x = 176^a-0.0003^(1-a);
which you can now rewrite as
0 < 176^a-0.0003^(1-a) < 12.5
The left boundary is reached at a = log(3/10000)/log(33/625) which is about 2.75792414361621 and the right boundary is reached at a approximately 0.4887342220443237643
But 0.488 etc is less than the lower bound of the constraint 0.5 < a < 0.75 so there is no solution to the equation.
You can plot (176^a-0.0003^(1-a))*0.016 over 0.5 to 0.75 and you will see that the value is everywhere greater than 0.2 which is the upper bound for z.
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