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CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization

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Abstract

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CUTEst, these updated versions feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD.

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Acknowledgments

We are extremely grateful to Roger Fletcher, Philip Gill, Bill Hager, Michal Kočvara, Michael Powell, Klaus Schittkowski and Elizabeth Wong for making their latest codes available to us so that we could build and test interfaces, and to two anonymous referees whose enthusiastic comments lead to a better paper. The work of the first author was supported by the EPSRC Grant EP/I013067/1. The work of the second author was supported by an NSERC Discovery Grant.

Author information

Authors and Affiliations

  1. Scientific Computing Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, UK

    Nicholas I. M. Gould

  2. Department of Mathematics and Industrial Engineering, École Polytechnique, and GERAD, Montréal, QC, Canada

    Dominique Orban

  3. Department of Mathematics, University of Namur, Namur, Belgium

    Philippe L. Toint

Authors
  1. Nicholas I. M. Gould
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  2. Dominique Orban
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  3. Philippe L. Toint
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Corresponding author

Correspondence to Nicholas I. M. Gould.

Appendices

Appendix 1: available tools

Separate evaluation tools are provided for unconstrained and constrained problems. Both unthreaded and threaded versions are available when this is relevant. See the appropriate man page for full details.

Unconstrained problems:

cutest_udimen (both threaded and unthreaded)

determine the number of variables.

cutest_usetup (unthreaded) and cutest_usetup_threaded (threaded)

setup internal data structures and determine variable bounds.

cutest_unames (both threaded and unthreaded)

determine the names of the problem and the variables.

cutest_uvartype (both threaded and unthreaded)

determine whether the variables are continuous or discrete.

cutest_udimsh (both threaded and unthreaded)

determine the number of nonzeros in the sparse Hessian.

cutest_udimse (both threaded and unthreaded)

determine the number of nonzeros in the finite-element Hessian.

cutest_ufn (unthreaded) and cutest_ufn_threaded (threaded)

evaluate the objective function value.

cutest_ugr (unthreaded) and cutest_ugr_threaded (threaded)

evaluate the gradient of the objective function.

cutest_uofg (unthreaded) and cutest_uofg_threaded (threaded)

evaluate both the values and gradients of the objective function.

cutest_udh (unthreaded) and cutest_udh_threaded (threaded)

evaluate the Hessian of the objective function as a dense matrix.

cutest_ugrdh (unthreaded) and cutest_ugrdh_threaded (threaded)

evaluate the objective gradient and dense Hessian.

cutest_ushp (both threaded and unthreaded)

evaluate the sparsity pattern of the Hessian of the objective function.

cutest_ush (unthreaded) and cutest_ush_threaded (threaded)

evaluate the Hessian of the objective function as a sparse matrix.

cutest_ugrsh (unthreaded) and cutest_ugrsh_threaded (threaded)

evaluate the objective gradient and sparse Hessian.

cutest_ueh (unthreaded) and cutest_ueh_threaded (threaded)

evaluate the Hessian of the objective function as a finite-element matrix.

cutest_ugreh (unthreaded) and cutest_ugreh_threaded (threaded)

evaluate the objective gradient and finite-element Hessian.

cutest_uhprod (unthreaded) and cutest_uhprod_threaded (threaded)

evaluate the product of the Hessian of the objective function with a vector.

cutest_ubandh (unthreaded) and cutest_ubandh_threaded (threaded)

obtain the part of the Hessian of the objective that lies within a specified

band.

cutest_ureport (unthreaded) and cutest_ureport_threaded (threaded)

discover how many evaluations have occured and how long this has taken.

cutest_uterminate (both unthreaded and threaded)

remove internal data structures when they are no longer needed.

Constrained problems:

cutest_cdimen (both threaded and unthreaded)

determine the number of variables and constraints.

cutest_csetup (unthreaded) and cutest_csetup_threaded (threaded)

setup internal data structures and determine variable and constraint bounds.

cutest_cnames (both threaded and unthreaded)

determine the names of the problem, the variables and the constraints.

cutest_connames (both threaded and unthreaded)

determine the names of the constraints.

cutest_cvartype (both threaded and unthreaded)

determine whether the variables are continuous or discrete.

cutest_cdimsj (both threaded and unthreaded)

determine the number of nonzeros in sparse constraint Jacobian.

cutest_cdimsh (both threaded and unthreaded)

determine the number of nonzeros in the sparse Hessian.

cutest_cdimse (both threaded and unthreaded)

determine the number of nonzeros in the finite-element Hessian.

cutest_cfn (unthreaded) and cutest_cfn_threaded (threaded)

evaluate the objective function and constraint values.

cutest_cgr (unthreaded) and cutest_cgr_threaded (threaded)

evaluate the gradients of the objective function and constraints.

cutest_cofg (unthreaded) and cutest_cofg_threaded (threaded)

evaluate both the value and gradient of the objective function.

cutest_cofsg (unthreaded) and cutest_cofsg_threaded (threaded)

evaluate both the value and sparse gradient of the objective function.

cutest_csgr (unthreaded) and cutest_csgr_threaded (threaded)

evaluate the sparse gradients of the objective function and constraints.

cutest_ccfg (unthreaded) and cutest_ccfg_threaded (threaded)

evaluate the values and gradients of the constraints.

cutest_ccfsg (unthreaded) and cutest_ccfsg_threaded (threaded)

evaluate the values and sparse gradients of the constraints.

cutest_ccifg (unthreaded) and cutest_ccifg_threaded (threaded)

evaluate the value and gradient of an individual constraint.

cutest_clfg (unthreaded) and cutest_clfg_threaded (threaded)

evaluate both the value and gradient of the Lagrangian function.

cutest_ccifsg (unthreaded) and cutest_ccifsg_threaded (threaded)

evaluate the value and sparse gradient of an individual constraint.

cutest_cdh (unthreaded) and cutest_cdh_threaded (threaded)

evaluate the Hessian of the Lagrangian function as a dense matrix.

cutest_cidh (unthreaded) and cutest_cidh_threaded (threaded)

evaluate the Hessian of the objective function or an individual constraint

as a dense matrix.

cutest_cgrdh (unthreaded) and cutest_cgrdh_threaded (threaded)

evaluate the constraint Jacobian and Hessian of the Lagrangian function

as dense matrices.

cutest_cshp (both threaded and unthreaded)

evaluate the sparsity pattern of the Hessian of the Lagrangian function.

cutest_csh (unthreaded) and cutest_csh_threaded (threaded)

evaluate the Hessian of the Lagrangian function as a sparse matrix.

cutest_cshc (unthreaded) and cutest_cshc_threaded (threaded)

evaluate the Hessian of the Lagrangian function not including the

objective as a sparse matrix.

cutest_cish (unthreaded) and cutest_cish_threaded (threaded)

evaluate the Hessian of the objective function or an individual constraint

as a sparse matrix.

cutest_csgrsh (unthreaded) and cutest_csgrsh_threaded (threaded)

evaluate the constraint Jacobian and Hessian of the Lagrangian function

as sparse matrices.

cutest_ceh (unthreaded) and cutest_ceh_threaded (threaded)

evaluate the Hessian of the Lagrangian function as a finite-element

matrix.

cutest_csgreh (unthreaded) and cutest_csgreh_threaded (threaded)

evaluate the constraint Jacobian as a sparse matrix and the Hessian of

the Lagrangian function as a finite-element matrix.

cutest_chprod (unthreaded) and cutest_chprod_threaded (threaded)

evaluate the product of the Hessian of the Lagrangian function with a

vector.

cutest_chcprod (unthreaded) and cutest_chcprod_threaded (threaded)

evaluate the product of the Hessian of the Lagrangian function not

including the objective with a vector.

cutest_cjprod (unthreaded) and cutest_cjprod_threaded (threaded)

evaluate the product of the constraint Jacobian or its transpose with a

vector.

cutest_creport (unthreaded) and cutest_creport_threaded (threaded)

discover how many evaluations have occured and how long this has taken.

cutest_cterminate (both unthreaded and threaded)

remove internal data structures when they are no longer needed.

Both unconstrained problems and constrained problems:

cutest_probname (both threaded and unthreaded)

determine the name of the problem.

cutest_varnames (both threaded and unthreaded)

determine the names of the variables.

A call to cutest_u/csetup[_threaded] must precede calls to any other evaluation tool with the exception of cutest_u/cdimen. Once cutest_u/cterminate[_threaded] has been called, no further calls should be made without first recalling cutest_u/csetup[_threaded].

Appendix 2: Matlab interfaces

The updated Matlab tools are described in Table 1.

Table 1 Available Matlab tools
Full size table

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Gould, N.I.M., Orban, D. & Toint, P.L. CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization. Comput Optim Appl 60, 545–557 (2015). https://doi.org/10.1007/s10589-014-9687-3

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