Best approximate solutions of inconsistent linear inequality systems

Miguel A. Goberna (1) , Jean-Baptiste Hiriart-Urruty (2) , Marco Antonio Lopez Cerda (3)

1 E-ALIC-OR - Department of Statistics and Operations Research
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Universidad de Alicante

This paper is intended to characterize three types of best approximate solutions for inconsistent linear inequality systems with an arbitrary number of constraints. It also gives conditions guaranteeing the existence of best uniform solutions and discusses potential applications.

Mots clés: Linear inequality systems; Best uniform solutions; Best L 1 solutions-best least squares solutions

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Miguel A. Goberna, Jean-Baptiste Hiriart-Urruty, Marco Antonio Lopez Cerda. Best approximate solutions of inconsistent linear inequality systems. Vietnam Journal of Mathematics, 2018, 46 (2), pp.271-284. ⟨10.1007/s10013⟩. ⟨hal-01975734⟩