Penalty schemes with inertial effects for monotone inclusion problems. (3rd June 2017)

• Record Type: Journal Article
• Authors: Boţ, Radu Ioan; Csetnek, Ernö Robert
• Is Part Of: Optimization. Volume 66:Number 6(2017)
• Page Start: 965
• Page End: 982
• Publication Date: 2017-06-03
• Subjects: Maximally monotone operator -- Fitzpatrick function -- resolvent -- Lipschitz continuous operator -- forward–backward-forward algorithm -- subdifferential -- Fenchel conjugate; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1181759
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a monotone and Lipschitz continuous operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the monotone inclusion problem, provided a condition expressed via the Fitzpatrick function of the operator describing the underlying set of the normal cone is verified. Under strong monotonicity assumptions we can even show strong nonergodic convergence of the iterates. This approach constitutes the starting point for investigating from a similar perspective monotone inclusion problems involving linear compositions of parallel-sum operators and, further, for the minimization of a complexly structured convex objective function subject to the set of minima of another convex and differentiable function.