We study online convex optimization with constraints consisting of multiple functional and a relatively simple constraint set, such as Euclidean ball. As enforcing the at each time step through projections is computationally challenging in general, we allow decisions to violate but aim achieve low regret cumulative violation over horizon T steps. First-order methods an O(sqrt{T}) O(1) violation...

In the setting adopted by Edmond and Thibault [Mathematical Programming 104 (2005), 347--373], we study a class of perturbed sweeping processes. Under suitable assumptions, obtain two solution existence theorems for processes with constraint sets being prox-regular sublevel sets. The results are applied to analyzing behavior some concrete mechanical processes, which appear first time in this pa...

In this articlewe discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets.We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state depen...

We introduce in the context of Asplund spaces, a new class of φ-regular functions. This new concept generalizes the one of prox-regularity introduced by Poliquin & Rockafellar (2000) in R and extended to Banach spaces by Bernard & Thibault (2004). In particular, the class of φ-regular functions includes all lower semicontinuous convex functions, all lower-C functions, and convexly C−composite f...