Entries for these benchmarks must record the average number number of force calls as force_calls in benchmark.dat, the maximum number of force calls as force_calls_max, the minimum number of force calls as force_calls_min, and the number of failed minimizations as nfailed
This benchmark tests the performance of optimizers starting from 1000 randomly generated LennardJones 38 clusters. A tar file containing the structures is here: lj38.tgz.
The L2 norm of the force must be reduced to at least 0.01 energy / distance. The maximum number of force calls that may be made cannot exceed 10,000. Runs that exceed the maximum number of force calls or fail to converge for any other reason are considered failed.
Entry  <N>  min N  max N  Failed 

optim
Comments:
The LBFGS memory length was set to 100 steps and the maximum move distance
was 0.2 distance units. Steps that increase energy are never accepted. This
is enforced by ensuring the step direction points downhill and, if necesary,
reducing the step size.

176  90  421  0 
pelelbfgsM100maxstep0.2
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM100maxstep0.2.tgz 
179  90  540  0 
eonlbfgs
Comments:
LBFGS with an initial diagonal inverse hessian equal to 0.004 distance squared
per energy. The memory length was set to 100 steps and the maximum move
distance was 0.2 distance units. The LBFGS history was reset when the angle
between the descent direction and the force became greater than 90º or a
step greater than the max move was taken.

181  90  405  0 
pelelbfgsM20maxstep0.1
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM20maxstep0.1.tgz 
222  116  507  0 
pelelbfgsM4maxstep0.2
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM4maxstep0.2.tgz 
230  100  620  0 
scipylbfgs^{1}
Date: 28 Aug 2013 Contributor: Jacob Stevenson Input files: scipylbfgs.tgz 
230  105  545  0 
pelelbfgsM10maxstep0.1
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM10maxstep0.1.tgz 
235  115  523  0 
pelelbfgsM4maxstep0.1
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM4maxstep0.1.tgz 
249  127  575  0 
pelelbfgsM1maxstep0.1
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM1maxstep0.1.tgz 
287  132  712  0 
aselbfgs^{1}
Date: 27 Aug 2013 Contributor: Sam Chill Input files: aselbfgs.tgz 
355  166  9317  1 
pelelbfgsM4maxstep0.05
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgsM4maxstep0.05.tgz 
379  200  773  0 
aselbfgslinesearch^{1}
Date: 27 Aug 2013 Contributor: Sam Chill Input files: aselbfgslinesearch.tgz 
417  239  862  0 
eoncg
Date: 24 Jun 2013 Contributor: Sam Chill Code: eonr2025.tgz Input files: eoncg.tgz 
453  207  1153  0 
eonsdtwopoint
Comments:
This steepest descent algoirthm uses the Barzilai and Borwein method for
determining the step size. The next position is determinied by
$$ x_{k+1} = x_k  \mathbf{S}_k g_k $$
where the step size $\mathbf{S}_k$ is
$$ S_k = \alpha_k \mathbf{I} $$
where $\mathbf{I}$ is the identity matrix and $\alpha_k$ is given by
$$ \alpha_k = \frac{\Delta x \cdot \Delta x}{\Delta x \cdot \Delta g} $$
with $\Delta x = x_k  x_{k1}$ and $\Delta g = g_k  g_{k1}$. For this
problem, $\alpha_0$ was set to 0.001.

539  182  2502  0 
asefire^{1}
Date: 23 Aug 2013 Contributor: Sam Chill Input files: asefire.tgz 
656  208  1000  0 
eonfire
Date: 24 Jun 2013 Contributor: Sam Chill Code: eonr2025.tgz Input files: eonfire.tgz 
731  227  2918  0 
eonqm
Date: 24 Jun 2013 Contributor: Sam Chill Code: eonr2025.tgz Input files: eonqm.tgz 
3523  667  9929  23 
eonsd
Comments:
This steepest descent algoirthm calculates the step size by assuming a constant curvature
of the potential energy:
$$ x_{k+1} = x_k  \alpha g_k $$
where $x_k$ is the current position, $g_k$ is the current gradient and $\alpha = 0.001$.

4901  1355  9982  96 
Show/Hide Additional Entries... 
This benchmark tests the performance of optimizers starting from 100 FCC bulk Morse structures that have been slightly perturbed from their equilibrium lattice positions. A tar file containing the structures is here: morsebulk.tgz.
$$ U(r) = D_e ( 1  e^{a(rr_e)})^2 $$where $D_e=0.7102$ eV, $r_e=2.8970$ Ang, and $a=1.6047$ Ang$^{1}$.
The norm of the force must be reduced to at least 1e3 eV/Ang
Entry  <N>  min N  max N 

optim
Comments:
The LBFGS memory length was set to 100 steps and the maximum move distance
was 2.0 distance units. Steps that increase energy are never accepted. This
is enforced by ensuring the step direction points downhill and, if necesary,
reducing the step size.

46  21  80 
pelelbfgs
Date: 06 Aug 2014 Contributor: Code: pelea68ec5.tgz Input files: pelelbfgs.tgz 
51  24  84 
eonlbfgs^{1}
Comments:
LBFGS with an initial diagonal inverse hessian equal to 0.04 distance squared
per energy. The memory length was set to 100 steps and the maximum move
distance was 0.2 distance units. The LBFGS history was reset when the angle
between the descent direction and the force became greater than 90º or a
step greater than the max move was taken.

52  35  81 
aselbfgs^{1}
Date: 26 Aug 2013 Contributor: Sam Chill Input files: aselbfgs.tgz 
54  35  91 
eonsdtwopoint^{1}
Comments:
This steepest descent algoirthm uses the Barzilai and Borwein method for
determining the step size. The next position is determinied by
$$ x_{k+1} = x_k  \mathbf{S}_k g_k $$
where the step size $\mathbf{S}_k$ is
$$ S_k = \alpha_k \mathbf{I} $$
where $\mathbf{I}$ is the identity matrix and $\alpha_k$ is given by
$$ \alpha_k = \frac{\Delta x \cdot \Delta x}{\Delta x \cdot \Delta g} $$
with $\Delta x = x_k  x_{k1}$ and $\Delta g = g_k  g_{k1}$. For this
problem, $\alpha_0$ was set to 0.04.

64  28  138 
eoncg^{1}
Date: 28 May 2014 Contributor: Sam Chill Input files: eoncg.tgz 
106  67  183 
asefire^{1}
Date: 23 Aug 2013 Contributor: Sam Chill Input files: asefire.tgz 
147  102  216 
eonfire^{1}
Comments:
LBFGS with an initial diagonal inverse hessian equal to 0.01 distance squared
per energy. At each step after the initial, the initial inverse hessian, which
determines the scale of the problem, is updated according to:
$$ H_0 = \frac{\Delta x \cdot \Delta x}{\Delta x \cdot \Delta g} $$
with $\Delta x = x_k  x_{k1}$ and $\Delta g = g_k  g_{k1}$.
The memory length was set to 100 steps and the maximum move
distance was 0.2 distance units. The LBFGS history was reset when the angle
between the descent direction and the force became greater than 90º or a
step greater than the max move was taken.

156  107  212 
eonsd^{1}
Comments:
This steepest descent algoirthm calculates the step size by assuming a constant curvature
of the potential energy:
$$ x_{k+1} = x_k  \alpha g_k $$
where $x_k$ is the current position, $g_k$ is the current gradient and $\alpha = 0.001$.

196  95  360 