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A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints

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Abstract

Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified in a priori given order fixed by the nature of the problem are studied. Moreover, if a constraint is not satisfied at a point, then the remaining constraints and the objective function can be undefined at this point. The constrained problem is reduced to a discontinuous unconstrained problem by the index scheme without introducing additional parameters or variables. A new geometric method using adaptive estimates of local Lipschitz constants is introduced. The estimates are calculated by using the local tuning technique proposed recently. Numerical experiments show quite a satisfactory performance of the new method in comparison with the penalty approach and a method using a priori given Lipschitz constants.

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Authors and Affiliations

  1. DEIS, University of Calabria, Via P. Bucci, 42C, 87036, Rende, (CS), Italy

    Yaroslav D. Sergeyev & Dmitri E. Kvasov

  2. Software Department, N.I. Lobatchevsky State University, Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev & Dmitri E. Kvasov

  3. Department of Mathematics, University of Calabria, Calabria, Italy

    Falah M. H. Khalaf

Authors
  1. Yaroslav D. Sergeyev
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  2. Dmitri E. Kvasov
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  3. Falah M. H. Khalaf
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Corresponding author

Correspondence to Yaroslav D. Sergeyev.

Additional information

This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, PRIN 2005017083-002, and RFBR 04-01-00455-a. The authors would like to thank anonymous referees for their subtle suggestions.

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Sergeyev, Y.D., Kvasov, D.E. & Khalaf, F.M.H. A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints. Optimization Letters 1, 85–99 (2007). https://doi.org/10.1007/s11590-006-0015-4

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  • DOI: https://doi.org/10.1007/s11590-006-0015-4

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