Сalculation of parameters estimates in homogeneous nested piecewise linear regression with alternating min and max functions

The article provides a brief review of publications on the implementation of nonlinear model forms in mathematical modeling of complex technical and socio-economic objects. Specifically, the following are considered: the dynamics of a nonlinear system with two degrees of freedom, consisting of a grounded linear oscillator connected to a light mass by a substantially nonlinear and nonlinearizable stiffness; the description of a new cybernetic structure that can help in understanding the specifics of timely deployment of recurring social phenomena; a new mathematical model for managing cyclical unemployment; configuration of several renewable energy systems in an eco-industrial park, an economic and mathematical model of production planning that takes into account its scale and the release of defective products. Homogeneous nested piecewise linear regressions with alternating min and max functions are studied. The tasks of calculating parameter estimates by minimizing the sums of absolute values of approximation errors are reduced to linear Boolean programming problems. The obtained optimal values of the Boolean variables of the problem reveal the order of external minimum and internal maximum in the considered nested models. A numerical illustrative case is solved.