# Find the minimum value of parameters that satisfy a set of conditions

I want to characterize the set of parameters that satisfy some conditions. One of the conditions is that the result of Solve/FindRoot is greater than zero. Example:

f[x_, a_, b_, c_] := a*x + Log[b*x - c] - Log[2 a + 10 c]
0<a<1 && 0.5<b<1&&1<c<2


In my example above, I want to find the minimum value of a, b and c that respect the given range such that x>0 (x given by the f[x,a,b,c] from Solve or FindRoot. Any ideas?

## 1 Answer

Perhaps you can use NMinimize:

NMinimize[
{
a+b+c,
f[x, a, b, c] == 0 && x>0 && 0<a<1 && 0.5<b<1 && 1<c<2
},
{x,a,b,c}
]


{1.5, {x -> 22., a -> 3.26705*10^-23, b -> 0.5, c -> 1.}}

• Thank you very much, Carl Woll. This was certainly what I needed. – Laura K Sep 4 '17 at 23:02
• Carl, what if I cannot find the zero of function f[x,a,b,c] cannot be solved for x analytically but it has the result of a numerical approximation? – Laura K Sep 6 '17 at 23:40