Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization

Samir Adly (1) , Florent Nacry (1) , Lionel Thibault (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper, we first provide counterexamples showing that sublevels of prox-regular functions and levels of differentiable mappings with Lipschitz derivatives may fail to be prox-regular. Then, we prove the uniform prox-regularity of such sets under usual verifiable qualification conditions. The preservation of uniform prox-regularity of intersection and inverse image under usual qualification conditions is also established. Applications to constrained optimization problems are given.

Mots clés: prox-regular set; hypomonotonicity; semiconvexity; metric regularity; constrained optimization; sweeping process

Domaines: Optimisation et contrôle [math.OC]

Samir Adly, Florent Nacry, Lionel Thibault. Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization. SIAM Journal on Optimization, 2016, 26 (1), pp.448-473. ⟨10.1137/15M1032739⟩. ⟨hal-01313215⟩