A stochastic inertial forward–backward splitting algorithm for multivariate monotone inclusions. (2nd June 2016)

• Record Type: Journal Article
• Authors: Rosasco, Lorenzo; Villa, Silvia; Vũ, Băng Công
• Is Part Of: Optimization. Volume 65:Number 6(2016)
• Page Start: 1293
• Page End: 1314
• Publication Date: 2016-06-02
• Subjects: Monotone inclusion -- monotone operator -- operator splitting -- cocoercive operator -- forward–backward algorithm -- composite operator -- duality -- primal–dual algorithm; 47H05 -- 49M29 -- 49M27 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1127371
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We propose an inertial forward–backward splitting algorithm to compute a zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in real Hilbert spaces of the sequence of iterates to an optimal solution. Then, based on this analysis, we introduce two new classes of stochastic inertial primal–dual splitting methods for solving structured systems of composite monotone inclusions and prove their convergence. Our results extend to the stochastic and inertial setting various types of structured monotone inclusion problems and corresponding algorithmic solutions. Application to minimization problems is discussed.