Geodesic
Inverse optimization problem solving for ANN data mining models based on the epsilon-Lipschitz approach
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2022), pp. 74-83

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Data mining techniques in particular cases cannot give us answers to all questions appeared in terms of the concerned simulation model. In this paper we show how some of such questions can be formulated as global optimization problem with continuous ANN function. Difficulties with proving an ANN based function Lipschitz continuity and Lipschitz constant estimating in some cases makes searching for the global minimum problematic since continuity does not guarantee us Lipschitz inequality holding. As a result, we are not able to apply conventional techniques. In this paper we propose the use of modified methods based on the $\varepsilon $- Lipschitz property for finding the global minimum because it requires only objective function continuity. As the example we analyze an ANN based prediction model for calculating metal level in human depending on metal level in drinking water, obtain associated optimization problem and show numerical results based on extended Strongin algorithm.
Keywords: ANN modeling, data mining, continuous function, global optimization, extended Strongin algorithm. 
@article{VTPMK_2022_2_a5,
     author = {S. V. Novikova and P. A. Chernyshevsky},
     title = {Inverse optimization problem solving for {ANN} data mining models based on the {epsilon-Lipschitz} approach},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {74--83},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_2_a5/}
}
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S. V. Novikova; P. A. Chernyshevsky. Inverse optimization problem solving for ANN data mining models based on the epsilon-Lipschitz approach. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2022), pp. 74-83. http://geodesic.mathdoc.fr/item/VTPMK_2022_2_a5/