Geodesic
Two modifications of extension of Piyavskii's global optimization algorithm to a function continuous on a compact interval and its convergence
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2021), pp. 70-85

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R.J. Vanderbei in his works proves that any continuous on a compact set function has the $\varepsilon $-Lipschitz property which extends conventional Lipschitz continuity. Based on this feature Vanderbei proposed one extension of Piyavskii’s global optimization algorithm to the continuous function case. In this paper we propose one modification of the Vanderbei’s algorithm for a positive $\varepsilon $-constant and another modification for a positive $\varepsilon $-constant and $\varepsilon $ value independent termination condition. We prove proposed methods convergence and perform several computational experiments with designed software for known test functions.
Keywords: $\varepsilon$-Lipschitz continuity, continuous function, global optimization
Mots-clés : algorithm convergence. 
@article{VTPMK_2021_3_a5,
     author = {V. I. Zabotin and P. A. Chernyshevsky},
     title = {Two modifications of extension of {Piyavskii's} global optimization algorithm to a function continuous on a compact interval and its convergence},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {70--85},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_3_a5/}
}
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V. I. Zabotin; P. A. Chernyshevsky. Two modifications of extension of Piyavskii's global optimization algorithm to a function continuous on a compact interval and its convergence. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2021), pp. 70-85. http://geodesic.mathdoc.fr/item/VTPMK_2021_3_a5/