Related papers: Optimal Parallel Algorithms for Convex Hulls in 2D…

When training large machine learning models with many variables or parameters, a single machine is often inadequate since the model may be too large to fit in memory, while training can take a long time even with stochastic updates. A…

Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…

Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…

We present a real-time method for robust estimation of multiple instances of geometric models from noisy data. Geometric models such as vanishing points, planar homographies or fundamental matrices are essential for 3D scene analysis.…

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…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…

We give in this paper a convergence result concerning parallel synchronous algorithm for nonlinear fixed point problems with respect to the euclidian norm in $\Rn$. We then apply this result to some problems related to convex analysis like…

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature…

We investigate the theoretical limits of pipeline parallel learning of deep learning architectures, a distributed setup in which the computation is distributed per layer instead of per example. For smooth convex and non-convex objective…

We present a novel GPU-accelerated implementation of the QuickHull algorihtm for calculating convex hulls of planar point sets. We also describe a practical solution to demonstrate how to efficiently implement a typical Divide-and-Conquer…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

As deep learning becomes more expensive, both in terms of time and compute, inefficiencies in machine learning (ML) training prevent practical usage of state-of-the-art models for most users. The newest model architectures are simply too…

The goal of this paper is twofold. First, it explores hybrid evolutionary-swarm metaheuristics that combine the features of PSO and GA in a sequential, parallel and consecutive manner in comparison with their standard basic form: Genetic…

In this paper we study the limitations of parallelization in convex optimization. A convenient approach to study parallelization is through the prism of \emph{adaptivity} which is an information theoretic measure of the parallel runtime of…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…