A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity
Yura Malitsky, Matthew K. Tam
Abstract
In this work, we propose a simple modification of the forward-backward splitting method for finding a zero in the sum of two monotone operators. Our method converges under the same assumptions as Tseng's forward-backward-forward method, namely, it does not require cocoercivity of the single-valued operator. Moreover, each iteration only uses one forward evaluation rather than two as is the case for Tseng's method. Variants of the method incorporating a linesearch, relaxation and inertia, or a structured three operator inclusion are also discussed.
Topics & Concepts
MathematicsMonotone polygonOperator splittingOperator (biology)Simple (philosophy)Applied mathematicsRelaxation (psychology)Monotonic functionInertiaMathematical optimizationMathematical analysisGeometryPhilosophyChemistryGeneClassical mechanicsTranscription factorBiochemistryRepressorEpistemologySocial psychologyPhysicsPsychologyNumerical methods in inverse problemsOptimization and Variational AnalysisMatrix Theory and Algorithms