In this paper, we give two explicit examples of unbounded linear maximal monotone operators. The first unbounded linear maximal monotone operator S on l is skew. We show its domain is a proper subset of the domain of its adjoint S∗, and −S∗ is not maximal monotone. This gives a negative answer to a recent question posed by Svaiter. The second unbounded linear maximal monotone operator is the in...

Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications...

and Applied Analysis 3 4 strictly η-monotone if 〈 u − v, ηx, y > 0, ∀x, y ∈ H, x / y, u ∈ M x , v ∈ M ( y ) ; 2.5 5 strongly monotone if there exists a constant r > 0 satisfying 〈 u − v, x − y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.6 6 strongly η-monotone if there exists a constant r > 0 satisfying 〈 u − v, ηx, y ≥ r∥x − y∥2, ∀x, y ∈ H, u ∈ M x , v ∈ My; 2.7 7 maximal monotone resp., maxim...

We propose a stochastic Forward Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of them is cocoercive. We first prove the weak almost sure convergence of the proposed method. We then characterize the rate of convergence in expectation in the case of strongly monotone operators. Finally, we ...

In this paper, we suggest and analyze both explicit and implicit iterative schemes for two strongly positive operators and a nonexpansive mapping S on a Hilbert space. We also study explicit and implicit versions of iterative schemes for an inverse-strongly monotone mapping T and S by an extragradient-like approximation method. The viscosity approximation methods are employed to establish stron...