Related papers: A hybrid method for solving systems of operator in…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
The backward-backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…
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…
This paper introduces the first objective space algorithm which can exactly find all supported and non-supported non-dominated solutions to a mixed-integer multi-objective linear program with an arbitrary number of objective functions. This…
This work describes a new variant of projective splitting for solving maximal monotone inclusions and complicated convex optimization problems. In the new version, cocoercive operators can be processed with a single forward step per…
Projective splitting is a family of methods for solving inclusions involving sums of maximal monotone operators. First introduced by Eckstein and Svaiter in 2008, these methods have enjoyed significant innovation in recent years, becoming…
We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…
This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and…
We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning. We propose novel variants of stochastic Halpern iteration with recursive variance…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
The split feasibility problem is to find an element in the intersection of a closed set $C$ and the linear preimage of another closed set $D$, assuming the projections onto $C$ and $D$ are easy to compute. This class of problems arises…
We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the A Contrario reasoning when applied to the segmentation problem, and to…