Thank you for your interest in S2MPJ, a collection of test problems for benchmarking optimization software, available in Matlab, Python and Julia. The collection contains most of the problems in the CUTEst collection, making them accessible without any use of Fortran or translation from Fortran.
The collection provide simple tools to set up a problem's data structure and to evaluate its objective function and/or constraints as well as their derivatives.
A full description of the collection and associated tools is available in the paper 's2mpj.pdf'.
Due to a limitation on the length of displayed directory content in Github, only a
fraction of the test problems are listed when showing the content of the matlab_problems,
python_problems and julia_problems directories on the Github web site. The lists of all
available problems can be accessed in list_of_matlab_problems, list_of_python_problems and
list_of_julia_problems, respectively. The complete set of test problems can be obtained
by downloading all_matlab_problems.tar.gz, all_python_problems.tar.gz and/or
all_julia_problems.tar.gz.
To use S2MPJ in Matlab, download the contents of this repository, open Matlab and make sure the local directory containing the 's2mpjlib.m' file and its subdirectory 'matlab_problems' are in the Matlab path.
Suppose now we have an optimization code MyOptimizer.m which we would like to apply to
one on the S2MPJ problems, let's say PROBLEM.m. We
first setup the problem data structure, along with the
starting point and bounds on the variables by issuing the command
[ pb, pbm ] = PROBLEM( 'setup', args{:} );at the beginning of MyOptimizer.m, before any call to function/constraint
values or derivatives. In this call, args{:} is an optional comma-separated
list of problem-dependent arguments (such as problem's dimension, for
instance) identified by the string "$-PARAMETER" in the SIF file. If args{:}
is missing, setup is performed using the SIF file defaults. The starting point
is now given by pb.x0, the lower bounds by pb.xlower and the upper bounds by pb.xupper.
Every time values of the objective function, and possibly of its derivatives,
at the vector x are needed in MyOptimizer.m, they are obtained by
issuing one of the commands
fx = PROBLEM( 'fx', x );
[ fx, gx ] = PROBLEM( 'fgx', x );
[ fx, gx, Hx ] = PROBLEM( 'fgHx', x );The product of the objective function's Hessian (at x) times a
user-supplied vector v can be obtained by the command
Hxv = PROBLEM( 'fHxv', x, v );If the problem has constraints (other than bounds on the variables), their values (and that of derivatives, if desired) are obtained by one of the commands
cx = PROBLEM( 'cx', x );
[ cx, Jx ] = PROBLEM( 'cJx', x );
[ cx, Jx, Hx ] = PROBLEM( 'cJHx', x );The product of the constraints' Jacobian (at x) times v is computed
by issuing the command
Jxv = PROBLEM( 'cJxv', x, v );and the product of the Jacobian transposed times v is obtained by
Jxv = PROBLEM( 'cJtxv', x, v );The value (and derivatives) of the Lagrangian function L(x,y) at (x,y)
is obtained by one of the commands
Lxy = PROBLEM( 'Lxy', x, y );}
[ Lxy, Lgxy ] = PROBLEM( 'Lgxy', x, y );
[ Lxy, Lgxy, LHxy ] = PROBLEM( 'LgHxy', x, y );while the product of the Lagrangian's Hessian times a vector v
can be computed with the command
HLxyv = PROBLEM( 'HLxyv', x, y, v );The list of Matlab test problems is available in the "list_of_matlab_problems" file.
The use of the collection in Python is very similar to that described for Matlab.
After downloading the content of the repository, make sure the directory containing
the file "s2mpjlib.py" and the subdirectory 'python_problems" are in sys.path.
Consider now using the problem PROBLEM.py in an optimization code.
After importing the functions of the PROBLEM module by
from PROBLEM import *the setup of the problem is now performed by a call of the form
PROB = PROBLEM( args[:] )where args[:] is an optional comma separated list of problem-dependent
arguments. The subsequent evaluation tasks are then obtained by
calling one (or more) of
fx = PROB.fx( x )
fx, gx = PROB.fgx( x )
x, gx, Hx = PROB.fgHx( x )
Hxv = PROB.fHxv( x, v )
cx = PROB.cx( x )
cx, Jx = PROB.cJx( x )
cx, Jx, HXs = PROB.cJHx( x )
cJxv = PROB.cJxv( x, v )
cJtxv = PROB.cJtxv( x, v )
cIx = PROB.cIx( x, I )
cIx, cIJx = PROB.cIJx( x, I )
cIx, cIJx, cIJHx = PROB.cIJHx( x, I )
cIJv = PROB.cIJxv( x, v, I )
cIJtv = PROB.cIJtxv( x, v, I )
Lxy = PROB.Lxy( x, y )
Lxy, Lgxy = PROB.Lgxy( x, y )
Lxy, gLxy, HLxy = PROB.LgHxy( x, y )
LHxyv = PROB.LHxyv( x, y, v )
LIxy = PROB.LIxy( x, y, I )
LIxy, gLIxy = PROB.LIgxy( x, y, I )
LIxy, gLIxy, HLIxy = PROB.LIgHxy( x, y, I )
LIHxyv = PROB.LIHxyv( x, y, v, I )The list of Python test problems is available in the "list_of_python_problems" file.
After dowloading the content of the repository, make sure the directory containing
the file "s2mpjlib.jl" and the subdirectory 'python_problems" are in LOAD_PATH.
To use of the problem PROBLEM.jl in an optimization code, one then first includes the
problem as in
include( "PROBLEM.jl" )and the setup of the problem is performed by a call
pb, pbm = PROBLEM( "setup", args[:] )where args[:] is an optional comma separated list of
problem-dependent arguments. The subsequent evaluation tasks are
then obtained by calling one (or more) of
fx = PROBLEM( "fx", pbm, x )
fx, gx = PROBLEM( "fgx", pbm, x )
fx, gx, Hx = PROBLEM( "fgHx", pbm, x )
Hxv = PROBLEM( "fHxv", pbm x, v )
cx = PROBLEM( "cx", pbm, x )
cx, Jx = PROBLEM( "cJx", pbm, x )
cx, Jx, HXs = PROBLEM( "cJHx", pbm, x )
cJxv = PROBLEM( "cJxv", pbm, x, v )
cJtxv = PROBLEM( "cJtxv", pbm, x, v )
cIx = PROBLEM( "cIx", pbm, x, I )
cIx, cIJx = PROBLEM( "cIJx", pbm, x, I )
cIx, cIJx, cIJHx = PROBLEM( "cIJHx", pbm, x, I )
cIJv = PROBLEM( "cIJxv", pbm, x, v, I )
cIJtv = PROBLEM( "cIJtxv", pbm, x, v, I )
Lxy = PROBLEM( "Lxy", pbm, x, y )
Lxy, Lgxy = PROBLEM( "Lgxy", pbm, x, y )
Lxy, Lgxy, LgHxy = PROBLEM( "LgHxy", pbm, x, y )
LHxyv = PROBLEM( "LHxyv", pbm, x, y, v )
LIxy = PROBLEM( "LIxy", pbm, x, y, I )
LIxy, LIgxy = PROBLEM( "LIgxy(", pbm, x, y, I )
LIxy, LIgxy, LIgHxy = PROBLEM( "LIgHxy", pbm, x, y, I )
LIHxyv = PROBLEM( "LIHxyv", pbm, x, y, v, I )Note that pbm always occurs as the second input argument.
The list of Julia test problems is available in the "list_of_julia_problems" file.
We hope that S2MPJ will prove useful in your benchmarking. If you have any bug reports or comments, please feel free to email one of the toolbox authors:
Serge Gratton <serge.gratton@enseeiht.fr>
Philippe Toint <philippe.toint@unamur.be>