I have the requirements to minimize the following:
$ (f(x)_1 + f(x)_2 + f(x)_3) $
where:
$ 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!