Gradient Descent and the Nelder-Mead Simplex Algorithm
Gradient Descent and the Nelder-Mead Simplex Algorithm
Gradient Descent and the Nelder-Mead Simplex Algorithm
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Why minimise a function numerically?<br />
non-linear regression<br />
• Linear Regression:<br />
▫ Fitting function is linear with respect to <strong>the</strong><br />
parameters<br />
can be solved analytically (see Wikipedia)<br />
• Non-linear Regression:<br />
▫ Fitting function is non-linear with respect to <strong>the</strong><br />
parameters (e.g. f(x,α 1 ,α 2 ) = sin(α 1 x)+cos(α 2 x))<br />
Often no analytical solution<br />
Numerical optimisation or direct search
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