相关论文: An Experimental Comparison of Methods for Computin…

Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…

We develop a robust convex algorithm to select the regularization parameter in model selection. In practice this would be automated in order to save practitioners time from having to tune it manually. In particular, we implement and test…

The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…

We realize many sharp spectral bounds of the spectral radius of a nonnegative square matrix $C$ by using the largest real eigenvalues of suitable matrices of smaller sizes related to $C$ that are very easy to find. As applications, we give…

We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with…

This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex…

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…

Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that…

We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different…

Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…

The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…

The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…

We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However,…

Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…