2006-09-22 00:22:34 +08:00
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<HTML>
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>minimize command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>minimize etol ftol maxiter maxeval
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</PRE>
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<UL><LI>etol = stopping tolerance for energy (unitless)
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<LI>ftol = stopping tolerance for force (force units)
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<LI>maxiter = max iterations of minimizer
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<LI>maxeval = max number of force/energy evaluations
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>minimize 1.0e-4 1.0e-6 100 1000
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minimize 0.0 1.0e-8 1000 100000
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Perform an energy minimization of the system, by iteratively adjusting
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atom coordinates. Iterations are terminated when one of the stopping
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criteria is satisfied. At that point the configuration will hopefully
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2008-06-28 01:40:03 +08:00
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be in local potential energy minimum. More precisely, the
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2008-06-24 23:17:35 +08:00
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configuration should approximate a critical point for the objective
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function (see below), which may or may not be a local minimum.
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</P>
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<P>The minimization algorithm used is set by the
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<A HREF = "min_style.html">min_style</A> command. Other options are set by the
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<A HREF = "min_modify.html">min_modify</A> command. Minimize commands can be
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interspersed with <A HREF = "run.html">run</A> commands to alternate between
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2008-06-24 23:17:35 +08:00
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relaxation and dynamics. The minimizers bound the distance atoms move
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in one iteration, so that you can relax systems with highly overlapped
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atoms (large energies and forces) by pushing the atoms off of each
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other.
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2006-09-22 00:22:34 +08:00
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</P>
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2007-12-11 23:29:25 +08:00
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<P>Alternate means of relaxing a system are to run dynamics with a small
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or <A HREF = "fix_nve_limit.html">limited timestep</A>. Or dynamics can be run
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using <A HREF = "fix_viscous.html">fix viscous</A> to impose a damping force that
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slowly drains all kinetic energy from the system. The <A HREF = "pair_soft.html">pair_style
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soft</A> potential can be used to un-overlap atoms while
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running dynamics.
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</P>
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<P>A minimization involves an outer iteration loop which sets the search
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direction along which atom coordinates are changed. An inner
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iteration is then performed using a line search algorithm. The line
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search typically evaluates forces and energies several times to set
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new coordinates. Currently, a backtracking algorithm is used which
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may not be optimal in terms of the number of force evaulations
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performed, but appears to be more robust than previous line searches
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we've tried. The backtracking method is described in Nocedal and
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Wright's Numerical Optimization (Procedure 3.1 on p 41).
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</P>
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2008-06-24 23:17:35 +08:00
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<P>The objective function being minimized is the total potential energy
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of the system as a function of the N atom coordinates:
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2008-06-24 00:12:04 +08:00
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</P>
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<CENTER><IMG SRC = "Eqs/min_energy.jpg">
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</CENTER>
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<P>where the first term is the sum of all non-bonded <A HREF = "pair_style.html">pairwise
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interactions</A> including <A HREF = "kspace_style.html">long-range Coulombic
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interactions</A>, the 2nd thru 5th terms are
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<A HREF = "bond_style.html">bond</A>, <A HREF = "angle_style.html">angle</A>,
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<A HREF = "dihedral_style.html">dihedral</A>, and <A HREF = "improper_style.html">improper</A>
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interactions respectively, and the last term is energy due to
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<A HREF = "fix.html">fixes</A> which can act as constraints or apply force to atoms,
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such as thru interaction with a wall. See the discussion below about
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2008-06-24 23:24:58 +08:00
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how fix commands affect minimization.
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2008-06-24 00:12:04 +08:00
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</P>
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<P>The starting point for the minimization is the current configuration
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of the atoms.
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</P>
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<HR>
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<P>The minimization procedure stops if any of several criteria are met:
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</P>
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<UL><LI>the change in energy between outer iterations is less than <I>etol</I>
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<LI>the 2-norm (length) of the global force vector is less than the <I>ftol</I>
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<LI>the line search fails because the step distance backtracks to 0.0
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<LI>the number of outer iterations exceeds <I>maxiter</I>
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<LI>the number of total force evaluations exceeds <I>maxeval</I>
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</UL>
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2008-04-15 05:37:10 +08:00
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<P>For the first criterion, the specified energy tolerance <I>etol</I> is
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unitless; it is met when the energy change between successive
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iterations divided by the energy magnitude is less than or equal to
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the tolerance. For example, a setting of 1.0e-4 for <I>etol</I> means an
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energy tolerance of one part in 10^4.
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</P>
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<P>For the second criterion, the specified force tolerance <I>ftol</I> is in
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force units, since it is the length of the global force vector for all
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atoms, e.g. a vector of size 3N for N atoms. Since many of the
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components will be near zero after minimization, you can think of
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<I>ftol</I> as an upper bound on the final force on any component of any
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atom. For example, a setting of 1.0e-4 for <I>ftol</I> means no x, y, or z
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component of force on any atom will be larger than 1.0e-4 (in force
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units) after minimization.
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</P>
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<P>Either or both of the <I>etol</I> and <I>ftol</I> values can be set to 0.0, in
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which case some other criterion will terminate the minimization.
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2006-09-22 00:22:34 +08:00
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</P>
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<P>During a minimization, the outer iteration count is treated as a
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timestep. Output is triggered by this timestep, e.g. thermodynamic
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output or dump and restart files.
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</P>
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2008-04-15 05:37:10 +08:00
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<P>Following minimization, a statistical summary is printed that lists
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which convergence criterion caused the minimizer to stop, as well as
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information about the energy, force, final line search, and and
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iteration counts. An example is as follows:
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</P>
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<PRE>Minimization stats:
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Stopping criterion = max iterations
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Energy initial, next-to-last, final =
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-0.626828169302 -2.82642039062 -2.82643549739
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Force two-norm initial, final = 2052.1 91.9642
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Force max component initial, final = 346.048 9.78056
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Final line search alpha, max atom move = 2.23899e-06 2.18986e-05
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Iterations, force evaluations = 2000 12724
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</PRE>
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<P>The 3 energy values are for before and after the minimization and on
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the next-to-last iteration. This is what the <I>etol</I> parameter checks.
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</P>
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<P>The two-norm force values are the length of the global force vector
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before and after minimization. This is what the <I>ftol</I> parameter
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checks.
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</P>
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<P>The max-component force values are the absolute value of the largest
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component (x,y,z) in the global force vector.
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</P>
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<P>The alpha parameter for the line-search, when multiplied by the max
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force component (on the last iteration), gives the max distance any
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atom moved during the last iteration. Alpha will be 0.0 if the line
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search could not reduce the energy. Even if alpha is non-zero, if the
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"max atom move" distance is tiny compared to typical atom coordinates,
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then it is possible the last iteration effectively caused no atom
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movement and thus the evaluated energy did not change and the
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minimizer terminated. Said another way, even with non-zero forces,
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it's possible the effect of those forces is to move atoms a distance
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less than machine precision, so that the energy cannot be further
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reduced.
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</P>
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<P>The iterations and force evaluation values are what is checked by the
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<I>maxiter</I> and <I>maxeval</I> parameters.
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</P>
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<HR>
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2010-04-28 06:09:09 +08:00
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<P>IMPORTANT NOTE: There are several force fields in LAMMPS which have
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discontinuities or other approximations which may prevent you from
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performing an energy minimization to high tolerances. For example,
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you should use a <A HREF = "pair_style.html">pair style</A> that goes to 0.0 at the
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cutoff distance when performing minimization (even if you later change
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it when running dynamics). If you do not do this, the total energy of
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the system will have discontinuities when the relative distance
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between any pair of atoms changes from cutoff+epsilon to
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cutoff-epsilon and the minimizer may behave poorly. Some of the
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manybody potentials use splines and other internal cutoffs that
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inherently have this problem. The <A HREF = "kspace_style.html">long-range Coulombic
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styles</A> (PPPM, Ewald) are approximate to within the
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user-specified tolerance, which means their energy and forces may not
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agree to a higher precision than the Kspace-specified tolerance. In
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all these cases, the minimizer may give up and stop before finding a
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minimum to the specified energy or force tolerance.
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2008-04-15 05:37:10 +08:00
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</P>
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<P>Note that a cutoff Lennard-Jones potential (and others) can be shifted
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so that its energy is 0.0 at the cutoff via the
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2010-05-07 23:11:21 +08:00
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<A HREF = "pair_modify.html">pair_modify</A> command. See the doc pages for
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inidividual <A HREF = "pair_style.html">pair styles</A> for details. Note that
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Coulombic potentials always have a cutoff, unless versions with a
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long-range component are used (e.g. <A HREF = "pair_lj.html">pair_style
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lj/cut/coul/long</A>). The CHARMM potentials go to 0.0 at
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the cutoff (e.g. <A HREF = "pair_charmm.html">pair_style lj/charmm/coul/charmm</A>),
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as do the GROMACS potentials (e.g. <A HREF = "pair_gromacs.html">pair_style
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lj/gromacs</A>).
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2008-04-15 05:37:10 +08:00
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</P>
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<P>If a soft potential (<A HREF = "pair_soft.html">pair_style soft</A>) is used the
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Astop value is used for the prefactor (no time dependence).
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2006-09-22 00:22:34 +08:00
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</P>
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2009-10-31 04:07:50 +08:00
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<P>The <A HREF = "fix_box_relax.html">fix box/relax</A> command can be used to apply an
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external pressure to the simulation box and allow it to shrink/expand
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during the minimization.
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</P>
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<P>Only a few other fixes (typically those that apply force constraints)
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are invoked during minimization. See the doc pages for individual
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2007-06-26 08:03:39 +08:00
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<A HREF = "fix.html">fix</A> commands to see which ones are relevant.
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</P>
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2007-06-26 08:03:39 +08:00
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<P>IMPORTANT NOTE: Some fixes which are invoked during minimization have
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an associated potential energy. For that energy to be included in the
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total potential energy of the system (the quantity being minimized),
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you MUST enable the <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> option for
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that fix. The doc pages for individual <A HREF = "fix.html">fix</A> commands
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specify if this should be done.
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</P>
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2008-04-15 05:37:10 +08:00
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<HR>
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2006-09-22 00:22:34 +08:00
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<P><B>Restrictions:</B>
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</P>
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2007-06-26 08:03:39 +08:00
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<P>Features that are not yet implemented are listed here, in case someone
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2006-09-22 00:22:34 +08:00
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knows how they could be coded:
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</P>
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2007-03-28 00:56:45 +08:00
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<P>It is an error to use <A HREF = "fix_shake.html">fix shake</A> with minimization
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because it turns off bonds that should be included in the potential
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energy of the system. The effect of a fix shake can be approximated
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during a minimization by using stiff spring constants for the bonds
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and/or angles that would normally be constrained by the SHAKE
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algorithm.
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</P>
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2007-03-28 01:01:13 +08:00
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<P><A HREF = "fix_rigid.html">Fix rigid</A> is also not supported by minimization. It
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is not an error to have it defined, but the energy minimization will
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not keep the defined body(s) rigid during the minimization. Note that
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if bonds, angles, etc internal to a rigid body have been turned off
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(e.g. via <A HREF = "neigh_modify.html">neigh_modify exclude</A>), they will not
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contribute to the potential energy which is probably not what is
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desired.
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2006-09-22 00:22:34 +08:00
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</P>
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2007-12-11 23:29:25 +08:00
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<P>Pair potentials that produce torque on a particle (e.g. <A HREF = "pair_gran.html">granular
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potentials</A> or the <A HREF = "pair_gayberne.html">GayBerne
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potential</A> for ellipsoidal particles) are not
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relaxed by a minimization. More specifically, radial relaxations are
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induced, but no rotations are induced by a minimization, so such a
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system will not fully relax.
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</P>
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2006-09-22 00:22:34 +08:00
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "min_modify.html">min_modify</A>, <A HREF = "min_style.html">min_style</A>,
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<A HREF = "run_style.html">run_style</A>
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</P>
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<P><B>Default:</B> none
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</P>
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</HTML>
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