In this work, we use the methodology of robustness optimization to address a regression problem under data uncertainty. We formulate a robust counterpart in the sense of robustness optimization of this problem. We compute explicitly the stability radius under a suitable assumption by using Ascoli formula. We obtain a fractional programming problem. By Charnes-Cooper variable transformation, we transform this fractional programming problem into convex optimization problem which can be linear in some cases. We recall the robust counterpart of uncertain problem in the sense of robust optimization. We show under appropriate assumptions that the optimal solution set of the robust counterpart in the sense of robust optimization is equal to that of robustness optimization.

uncertainty, regression problem, robustness optimization, robust counterpart, stability radius.

Received: September 2, 2022;  Accepted: October 27, 2022; Published: March 29, 2023

How to cite this article: Moussa Barro, Ali Ouedraogo and Sado Traoré, Solving uncertain regression problem by using robustness optimization method, Far East Journal of Applied Mathematics 116(2) (2023), 73-97. http://dx.doi.org/10.17654/0972096023006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 

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