Abstract.
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a Hölder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.
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Received: April 2002 / Accepted: December 2002 Published online: March 21, 2003
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ID="⋆" This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, and RFBR 01–01–00587.
Key Words. global optimization – multiextremal constraints – local tuning – index approach
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Sergeyev, Y., Pugliese, P. & Famularo, D. Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints. Math. Program., Ser. A 96, 489–512 (2003). https://doi.org/10.1007/s10107-003-0372-z
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DOI: https://doi.org/10.1007/s10107-003-0372-z