Prox-Penalization and Splitting Methods for Constrained Variational Problems

This paper is concerned with the study of a class of prox-penalization methods for solving variational inequalities of the form Ax + NC (x) 0 where H is a real Hilbert space, A : H H is a maximal monotone operator and NC is the outward normal cone to a closed convex set C ⊂ H. Given Ψ : H → R ∪ {+∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter βn, we consider a diagonal proximal algorithm of the form xn = I + λn(A + βn∂Ψ) −1 xn−1, and an algorithm which alternates proximal steps with respect to A and penalization steps with respect to C and reads as xn = (I + λnβn∂Ψ)−1 (I + λnA)−1

• Type: Journal
• Year: 2011
• Where: SIAMJO
• Authors: Hedy Attouch, Marc-Olivier Czarnecki, Juan Peypouquet
• Keywords: Diagonal Proximal Algorithm, Maximal Monotone Operator, Outward Normal Cone, SIAMJO 2011, Software Engineering