93a65ca5-c1b4-4af3-92a3-8572a58e3437 111 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

References:

http://www.brnt.eu/phd/node10.html

α 0 >

reflection coefficient

1

0 β < 1 <

contraction coefficient

0.5

γ 1 >

expansion coefficient

2

Nelder-Mead optimization algorithm (AKA Downhill simplex) x# f simplex α β γ NelderMead.ref k 0 : n simplex length : check for input errors m simplex 1 el length : r m 1 + : n r ≠ need r num2str starting points as simplex concat error 0 if α 0 ≤ α must be > 0 error 0 if β 0 ≤ (β 1 ≥ (| β must be between 0 and 1 error 0 if γ 1 ≤ γ must be > 1 error 0 if 71 line x# G 1 n / x# i el (i 1 n sum * : x simplex : k 100 < F 011 mat : i 1 n range F i el x i el f eval : F i el F max ≡ h i : 0 if F i el F min ≡ l i : 0 if 31 line for F.m 1 n / F sum * eval : 1 n / F i el F.m - (2^(i 1 n sum * sqrt eval 1014 -^< break k k 1 + : if 21 line x' 1 α + (x G * α x h el * - eval : x' f x l el f < x'' 1 γ + (x' * γ x G * - eval : x'' f x l el f < x h el x'' : x h el x' : if 21 line flag 1 : i 1 n range i h ≠ x' f x i el f > 0 flag 0 : if 0 if for flag 1 ≡ x' f x h el f ≤ x h el x' : 0 if x'' β x h el * 1 β - (x G * + eval : x'' f x h el f > i 1 n range x i el 12 / x i el x l el + (* eval : for x h el x'' : if 31 line x h el x' : if 31 line if 51 line while x l el k 11 mat 21 mat 71 line :

x f 1 x 1 el - (2^10 x 2 el x 1 el (2^- (2^* + :

1121 mat f 0

x# f simplex NelderMead

x# f simplex ε.σF NelderMead

x f 1 - 0.5 - 21 mat 0.5 - 1.5 21 mat 0.5 121 mat 31 mat 1 0.5 2 NelderMead.ref 1.00172 0.9897 21 mat 8611 mat 21 mat

x# f simplex ε.σF α β γ NelderMead

x# f simplex ε.σF α β γ n.iters show.iters show.summary save.summary NelderMead

x f 1 - 0.5 - 21 mat 0.5 - 1.5 21 mat 0.5 121 mat 13 mat 105 -^NelderMead 1.00183 0.98991 21 mat

<<< NOTE: symplex's values must be placed in a row vector

x Rosenbrock 1 x 1 el - 10 sqrt x 2 el x 1 el (2^- (* 21 mat - :

1121 mat Rosenbrock 0021 mat

x R x Rosenbrock i el (2^(i 12 sum :

x R 1 - 0.5 - 21 mat 0.5 - 1.5 21 mat 0.5 121 mat 31 mat 1 0.5 2 NelderMead.ref 1.00172 0.9897 21 mat 8611 mat 21 mat

x Rosenbrock 1 - 0.5 - 21 mat 0.5 - 1.5 21 mat 0.5 121 mat 13 mat 1014 -^000 NelderMead 1.00172 0.9897 21 mat