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 Pijavskiiís 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.

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