1,201 research outputs found
A first-order stochastic primal-dual algorithm with correction step
We investigate the convergence properties of a stochastic primal-dual
splitting algorithm for solving structured monotone inclusions involving the
sum of a cocoercive operator and a composite monotone operator. The proposed
method is the stochastic extension to monotone inclusions of a proximal method
studied in {\em Y. Drori, S. Sabach, and M. Teboulle, A simple algorithm for a
class of nonsmooth convex-concave saddle-point problems, 2015} and {\em I.
Loris and C. Verhoeven, On a generalization of the iterative soft-thresholding
algorithm for the case of non-separable penalty, 2011} for saddle point
problems. It consists in a forward step determined by the stochastic evaluation
of the cocoercive operator, a backward step in the dual variables involving the
resolvent of the monotone operator, and an additional forward step using the
stochastic evaluation of the cocoercive introduced in the first step. We prove
weak almost sure convergence of the iterates by showing that the primal-dual
sequence generated by the method is stochastic quasi Fej\'er-monotone with
respect to the set of zeros of the considered primal and dual inclusions.
Additional results on ergodic convergence in expectation are considered for the
special case of saddle point models
Inverse Problems for Nonlinear Quasi-Variational Inequalities with an Application to Implicit Obstacle Problems of -Laplacian Type
The primary objective of this research is to investigate an inverse problem
of parameter identification in nonlinear mixed quasi-variational inequalities
posed in a Banach space setting. By using a fixed point theorem, we explore
properties of the solution set of the considered quasi-variational inequality.
We develop a general regularization framework to give an existence result for
the inverse problem. Finally, we apply the abstract framework to a concrete
inverse problem of identifying the material parameter in an implicit obstacle
problem given by an operator of -Laplacian type
ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS
In this paper, a new iterative method for solving convex minimization problems over the set of common fixed points of quasi-nonexpansive and demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. As an application, we shall utilize our results to solve quadratic optimization problems involving bounded linear operator. Our theorems are significant improvements on several important recent results
- …