Global optimisation procedures for solving systems of Hölder equations-inequations
Djaouida Guettal, Mohamed Rahal · International Journal of Computing Science and Mathematics · 2023
In this paper, Shubert-Piyavskii's algorithm (SPA) proposed for solving problems of global optimisation with Lipschitz data is extended to the class of Hölder global optimisation problems with several variables. It can be applied to solving systems of Hölder equations-inequations over a compact set of Rn, by transforming the original systems into an equivalent Hölder global optimisation problem. We use a procedure for partitioning and eliminating hyper-surfaces without interest by constructing piecewise constant minorant functions, which depend on piecewise parabolic cone minorant functions. The proposed algorithm is proven to have a finite convergence to the global optimum. Computational results on several standard examples are given.