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In this paper, we are concerned with geometric constraint solvers, i.e., with programs that find one or more solutions of a geometric constraint problem. If no solution exists, the solver is expected to announce that no solution has been…
Progressive dimensionality reduction algorithms allow for visually investigating intermediate results, especially for large data sets. While different algorithms exist that progressively increase the number of data points, we propose an…
During the last years, the emerging field of Augmented & Virtual Reality (AR-VR) has seen tremendousgrowth. At the same time there is a trend to develop low cost high-quality AR systems where computing poweris in demand. Feature points are…
We consider the following problem in computational geometry: given, in the d-dimensional real space, a set of points marked as positive and a set of points marked as negative, such that the convex hull of the positive set does not intersect…
One of the most significant challenges in Computing Determinant of Rectangular Matrices is high time complexity of its algorithm. Among all definitions of determinant of rectangular matrices, used definition has special features which make…
This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
In this paper, we consider the computation of the degree of the Dieudonn\'e determinant of a linear symbolic matrix $A = A_0 + A_1 x_1 + \cdots + A_m x_m$, where each $A_i$ is an $n \times n$ polynomial matrix over $\mathbb{K}[t]$ and…
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…
With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points…
Recent advances in deep learning have allowed neural networks (NNs) to successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains. One such application is time domain simulation, which…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
We prove the existence of an algorithm $A$ for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every sequence $\sigma$ of $n$ points and for every algorithm $A'$ in a certain class…