Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
Mathematical Programming: Series A and B
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
SIAM Journal on Control and Optimization
Convex analysis and variational problems
Convex analysis and variational problems
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
Dualization of Generalized Equations of Maximal Monotone Type
SIAM Journal on Optimization
A family of projective splitting methods for the sum of two maximal monotone operators
Mathematical Programming: Series A and B
A Parallel Splitting Method for Coupled Monotone Inclusions
SIAM Journal on Control and Optimization
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
On Weak Convergence of the Douglas-Rachford Method
SIAM Journal on Control and Optimization
Composition duality principles for mixed variational inequalities
Mathematical and Computer Modelling: An International Journal
Full length article: Attouch-Théra duality revisited: Paramonotonicity and operator splitting
Journal of Approximation Theory
Computational Optimization and Applications
A splitting algorithm for dual monotone inclusions involving cocoercive operators
Advances in Computational Mathematics
Journal of Mathematical Imaging and Vision
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The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal-dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators, and convergence results are established. These algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration. Comparisons with existing methods are made and applications to composite variational problems are demonstrated.