Frugal Splitting Operators: Representation, Minimal Lifting, and Convergence

Understand

We investigate frugal splitting operators for finite sum monotone inclusion problems.

• These operators utilize exactly one direct or resolvent evaluation of each operator of the sum, and the splitting operator's output is dictated by linear combinations of these evaluations' inputs and outputs.
• To facilitate analysis, we introduce a novel representation of frugal splitting operators via a generalized primal-dual resolvent.
• The representation is characterized by an index and four matrices, and we provide conditions on these that ensure equivalence between the classes of frugal splitting operators and generalized primal-dual resolvents.