I have the requirements to minimize the following:
$$ (f(x)_1 + f(x)_2 + f(x)_3) $$
$$ f(x)_1 = y_1 - (\exp(b+m_1) \times x) $$ $$ f(x)_2 = y_2 - (\exp(b+m_2) \times x) $$ $$ f(x)_3 = y_3 - (\exp(b+m_3) \times x) $$
given the range of $x$:
$$ a = 1.191206112 $$ $$ b = 1.321909214 $$ $$ x \in R \space|\space a \le x \le b $$
Is there a way to estimate the value of $x$ that returns the minimized sum of the three functions? As you can see, my $y$ and $m$ values are specific to the function but the $b$ is constant across all three.
Currently, I am testing random values between $[a,b]$ and recording the smallest sum. This takes about 50,000 iterations before I start approaching the asymptote. There has got to be a better way!