SOLVING UNCERTAIN REGRESSION PROBLEM BY USING ROBUSTNESS OPTIMIZATION METHOD
http://dx.doi.org/10.17654/0972096023006
Keywords:
uncertainty, regression problem, robustness optimization, robust counterpart, stability radiusAbstract
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.
Received: September 2, 2022
Accepted: October 27, 202
Published: March 29, 2023
References
G. Allaire, Analyse numérique et optimisation: une introduction à la modélisation mathématique et à la simulation, edition, Les Éditions de l’École Polytechnique, Paris, 2012.
D. Bertsimas, D. Pachamanova and S. Melvyn, Robust linear optimization under general norms, Oper. Res. Lett. 32 (2004), 510-516.
H. Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983.
F. L. Bauer, J. Stoer and C. Witzgall, Absolute and monotonic norms, Numer. Math. 3 (1961), 257-264.
A. Ben-Tal, L. El Ghaoui and A. Nemirovski, Robust optimization, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, 2009.
A. Ben-Tal and A. Nemirovski, Robust optimization methodology and applications, Math. Program. 92 (2002), 458-480.
J.-P. Crouzeix and J. A. Ferland, Algorithms for generalized fractional programming, Math. Program. 52 (1991), 191-207.
E. Carrizosa and J. Fliege, Generalized goal programming: polynomial methods and applications, Math. Program. 93 (2002), 281-303.
M. Ciligot-Travain, Sur une notion de robustesse, Ann. I.S.U.P. 56 (2012), 37-48.
W. Dinkelbach, On nonlinear fractional programming, Management Science 13 (1967), 492-498.
L. El Ghaoui and H. Lebret, Robust solutions to least-squares problems with uncertain data, SIAM J. Matrix Anal. Appl. 18 (1997), 1035-1064.
H. A. Hindi and S. P. Boyd, Robust solutions to and uncertain linear approximation problems using convex optimization, Proceedings of the American Control Conference 6 (1998), 3487-3491.
S. Schaible, Parameter-free convex equivalent and dual programs of fractional programming problems, Zeitschrift fur Operations Research 18 (1974), 187-196.
R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, Princeton University Press, Princeton, 1970.
M. Volle, Conjugaison par tranche et dualité de Toland, Optimization 18 (1987), 633-642.
H. Xu and C. Caramanis, Robust regression and Lasso, IEEE Trans. Inform. Theory 56 (2010), 3561-3574.
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