Non-convex sweeping processes involving maximal monotone operators. (2nd September 2017)

• Record Type: Journal Article
• Authors: Adly, Samir; Le, Ba Khiet
• Is Part Of: Optimization. Volume 66:Number 9(2017)
• Page Start: 1465
• Page End: 1486
• Publication Date: 2017-09-02
• Subjects: Sweeping process -- differential inclusion -- variational analysis -- maximal monotone operator -- non-smooth Lyapunov pairs; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1337765
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : By using a regularization method, we study in this paper the global existence and uniqueness property of a new variant of non-convex sweeping processes involving maximal monotone operators. The system can be considered as a maximal monotone differential inclusion under a control term of normal cone type forcing the trajectory to be always contained in the desired moving set. When the set is fixed, one can show that the unique solution is right-differentiable everywhere and its right-derivative is right-continuous. Non-smooth Lyapunov pairs for this system are also analysed.