666 research outputs found
A stochastic inertial forward-backward splitting algorithm for multivariate monotone inclusions
We propose an inertial forward-backward splitting algorithm to compute the
zero of a sum of two monotone operators allowing for stochastic errors in the
computation of the operators. More precisely, we establish almost sure
convergence in real Hilbert spaces of the sequence of iterates to an optimal
solution. Then, based on this analysis, we introduce two new classes of
stochastic inertial primal-dual splitting methods for solving structured
systems of composite monotone inclusions and prove their convergence. Our
results extend to the stochastic and inertial setting various types of
structured monotone inclusion problems and corresponding algorithmic solutions.
Application to minimization problems is discussed
Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions
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 to systems of coupled monotone inclusions are presented.
Our framework does not impose additional assumptions on the operators present
in the formulation, and it does not require knowledge of the norm of the linear
operators involved in the compositions or the inversion of linear operators
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