A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics

Samir Adly (1)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

The main concern of this paper is to investigate the Lipschitzian-like stability property (namely Aubin property) of the solution map of possibly nonmonotone variational systems with composite superpotentials. Using Mordukhovich coderivative criterion and a second-order subdifferential analysis, we provide simple and verifiable characterizations of this property in terms of the data involved in the problem. Applications are given in nonsmooth mechanics.

Mots clés: Limiting (Mordukhovich) coderivative; Parametric variational inequalities; Parametric hemivariational inequalities; Parametric generalized equation; Aubin property; Lipschitzian stability

Domaines: Optimisation et contrôle [math.OC]

Samir Adly. A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics. Journal of Optimization Theory and Applications, 2019, 180 (1), pp.62-90. ⟨10.1007/s10957-018-1293-6⟩. ⟨hal-02109951⟩