Related papers: Desingularization Algorithms: A Comparison from th…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
The article is about a "desingularization principle" common to various canonical desingularization algorithms in characteristic zero, and the roles played by the exceptional divisors in the underlying local construction. We compare…
Document image has been the area of research for a couple of decades because of its potential application in the area of text recognition, line recognition or any other shape recognition from the image. For most of these purposes…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a…
Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
A random search algorithm intended to solve discrete optimization problems is considered. We outline the main components of the algorithm, and then describe it in more detail. We show how the algorithm can be implemented on parallel…
Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
This monograph presents a class of algorithms called coordinate descent algorithms for mathematicians, statisticians, and engineers outside the field of optimization. This particular class of algorithms has recently gained popularity due to…
We give algorithms to construct the N\'eron Desingularization and the easy case from \cite{KK} of the General N\'eron Desingularization.
In recent years, significant advances have been made in the design and analysis of fully dynamic maximal matching algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…