Constructing non-elementary quasilinear regressions using mathematical programming apparatus

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Abstract

In non-elementary quasilinear regressions, the explanatory variables are first transformed using elementary functions, after which the pairs of resulting factors are again transformed using the non-elementary functions min and max. Such models are nonlinear in both factors and parameters, so even their estimation seems to be a complex computational task. And if the composition of the variables included in the model, as well as their elementary and non-elementary transformations, is unknown, then the complexity of the problem increases significantly. This study aims to solve this problem. Instead of labor-intensive exhaustive search procedures, a well-developed mathematical programming apparatus has been used recently. The method for constructing non-elementary quasilinear regressions is formalized as a mixed 0-1 integer linear programming problem. The proposed method is implemented in a special computer program. Its advantage is that the user can regulate the number of transformed variables during the construction process, so the program can be used both for solving simple control problems on ordinary personal computers and for processing large data arrays using cloud services. Non-elementary quasilinear regressions can be used to solve control problems in technical, socio-economic, medical and other systems.

About the authors

Mikhail Pavlovich Bazilevskiy

Irkutsk State Transport University

Email: mik2178@yandex.ru
Irkutsk

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