In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an approximate sense. Moreover, by sho...

Gossez type (D) operators are defined in non-reflexive Banach spaces and share with the subdifferential a topological related property, characterized by bounded nets. In this work we present new properties and characterizations of these operators. The class (NI) was defined after Gossez defined the class (D) and seemed to generalize the class (D). One of our main results is the proof that these...

For a maximal monotone operator T on a Hilbert space H and a closed subspace A of H, we consider the problem of finding (x, y ∈ T (x)) satisfying x ∈ A and y ∈ A⊥. An equivalent formulation of this problem makes use of the partial inverse operator of Spingarn. The resulting generalized equation can be solved by using the proximal point algorithm. We consider instead the use of hybrid proximal m...

Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0, and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B andW be maximal monotone operators on H such that the domains of B andW are included in C. Let 0 < k < 1, and let g be a k-contraction of H into itself. Let V be a γ -strongly monoto...

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward-backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as L. Rosasco DIBRIS, Univ...