Related papers: The upper-crossing/solution (US) algorithm for roo…
Autonomous sorting is a crucial task in industrial robotics which can be very challenging depending on the expected amount of automation. Usually, to decide where to sort an object, the system needs to solve either an instance retrieval…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
We develop the ultraspherical rectangular collocation (URC) method, a collocation implementation of the sparse ultraspherical method of Olver \& Townsend for two-point boundary-value problems. The URC method is provably convergent, the…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
We describe a subdivision algorithm for isolating the complex roots of a polynomial $F\in\mathbb{C}[x]$. Given an oracle that provides approximations of each of the coefficients of $F$ to any absolute error bound and given an arbitrary…
We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms. We devise a novel algorithm, referred to as Recursive One-Over-T SGD (ROOT-SGD), based on an easily…
The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in $2D$. Function extension plays a fundamental role…
In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…
We propose a graph-based sweep algorithm for solving the steady state, mono-energetic discrete ordinates on meshes of high-order curved mesh elements. Our spatial discretization consists of arbitrarily high-order discontinuous Galerkin…
In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
Neural architecture search (NAS) is an attractive approach to automate the design of optimized architectures but is constrained by high computational budget, especially when optimizing for multiple, important conflicting objectives. To…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…