This program provides Dynamic (gradient) and Pawlle's (not gradient) methods
for multi-variable function optimization
Consider next problem:
There are `n` points in `m`-dimension space.
The potential energy of pair of poits `(p_i, p_j)` is:
U_ij = (1/r_ij)^12 - (1/r_ij)^6
Total energy:
U_tot = Sum U_ij, i < j
Average energy for point:
U_at = 1/n U_tot
We want to minimaze `U_at`.
Considering `n m` vector as an argument for function, we are looking for best coordinates of points.
Actually, it finds only local minimums. For better results both methods are used.
`output.txt` is a results of applying both methods
`output1.txt` is a results of Pawlle's method
`output2.txt` is a results of Dynamic method
Pawlle's method:
s = {e1, e2, ..., e_q} -- set of basis vectors (for example, q = n m in this task)
answer -- current answer
prev_answer -- answer on the previous step
do {
prev_answer = answer
for i = 1 to q
lambda = argmin_lambda(answer + lambda * s_i)
answer = answer + lambda * s_i
for i = 1 to q-1
s_i = s_{i+1}
s_q = (answer - prev_answer)
s_q /= norm(s_q)
lambda = argmin_lambda(answer + lambda * s_i)
answer = answer + lambda * s_i
step++
if (step > q)
s = {e1, e2, ..., e_q}
} while (abs(answer - prev_answer) / answer > eps)
Moreover it uses some tricks with loops for better converge.
make- output.txt - for results
Copyright (C) 2013 Alexander Lapin
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Alexander Lapin, lapinra@gmail.com