Related papers: Splitting the Forward-Backward Algorithm: A Full C…
In this paper, we propose a stochastic version of the classical Tseng's forward-backward-forward method with inertial term for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued monotone operator…
An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually. The key tool in the development of this framework is the…
Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the…
We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…
We introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove…
In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
We propose a Boolean Linear Programming model for the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights(priorities) minimizing the total weighted completion time. Almost always an…
Monotone operator splitting is a powerful paradigm that facilitates parallel processing for optimization problems where the cost function can be split into two convex functions. We propose a generalized form of monotone operator splitting…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…
A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…
In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…
We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…