Related papers: Fast-Forwarding Stalling in Dykstra's Algorithm
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…
We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing quadratic. We give conditions for which convergence to the primal minimizer…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
We discuss several strategies to implement Dykstra's projection algorithm on NVIDIA's compute unified device architecture (CUDA). Dykstra's algorithm is the central step in and the computationally most expensive part of statistical…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…
Consider the setting where each vertex of a graph has a function, and communications can only occur between vertices connected by an edge. We wish to minimize the sum of these functions. For the case when each function is the sum of a…
This paper deals with constrained convex problems, where the objective function is smooth strongly convex and the feasible set is given as the intersection of a large number of closed convex (possibly non-polyhedral) sets. In order to deal…
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…
Feasibility problem aims to find a common point of two or more closed (convex) sets whose intersection is nonempty. In the literature, projection based algorithms are widely adopted to solve the problem, such as the method of alternating…
Recently, covariance descriptors have received much attention as powerful representations of set of points. In this research, we present a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the…
Stochastic Gradient Descent (SGD) is widely used in machine learning problems to efficiently perform empirical risk minimization, yet, in practice, SGD is known to stall before reaching the actual minimizer of the empirical risk. SGD…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…
Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…