Test problems for Lipschitz univariate global optimization with multiextremal
constraints
Development of
numerical algorithms for global optimization is strongly connected to the
problem of construction of test functions for studying and verifying validity
of these algorithms. Many of global optimization tests are taken from real-life
applications and for this reason complete information about them is not
available. In the paper
Famularo D., Sergeyev Ya.D., Pugliese P. (2002) Test problems for Lipschitz
univariate global optimization with multiextremal constraints, Stochastic and Global
Optimization, eds. G. Dzemyda, V. Saltenis, and A. Zilinskas,
Kluwer Academic Publishers, Dordrecht, 93-110.
Lipschitz univariate
constrained global optimization problems where both the objective function and
constraints can be multiextremal are considered. Two sets of test problems have been
introduced, in the first one both the objective function and constraints are
differentiable functions and in the second one they are non-differentiable.
Each series of tests contains 3 problems with one constraint, 4 problems with 2
constraints, 3 problems with 3 constraints, and one infeasible problem with 2
constraints. All the problems are shown in Figures. Lipschitz
constants and global solutions are given. For each problem it is indicated
whether the optimum is located on the boundary or inside a feasible subregion and the number of disjoint feasible subregions is given. Results of numerical experiments
executed with the introduced test problems using Pijavskii’s
method combined with a non-differentiable penalty function are also presented.
The version of this
paper that can be downloaded from this page has been carefully checked by D.E. Kvasov and F.M.H.
Khalaf. The authors thank them for eliminating misprints appeared in the
original paper.
Please have also a
look at our GKLS generator of classes of test functions with known local minima