SOLVING UNCERTAIN REGRESSION PROBLEM BY USING ROBUSTNESS OPTIMIZATION METHOD

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Résumé

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.

Mots-clés

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