Related papers: A Gr\"obner bases methodology for solving multiobj…
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
We present algorithms for computing the reduced Gr\"{o}bner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal.…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
We present an implementation of the algorithm for computing Groebner bases for operads due to the first author and A. Khoroshkin. We discuss the actual algorithms, the choices made for the implementation platform and the data…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients.…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently,…
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a…
We show herein that a pattern based on FGLM techniques can be used for computing Gr\"obner bases, or related structures, associated to linear codes. This Gr\"obner bases setting turns out to be strongly related to the combinatorics of the…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The…
Clear and concise code is necessary to ensure maintainability, so it is crucial that the software is as simple as possible to understand, to avoid bugs and, above all, vulnerabilities. There are many ways to enhance software without…
We report on an approach to integration-by-parts reduction based on Gr\"obner bases. We establish the underlying noncommutative rational double-shift algebra wherein the integration-by-parts relations form a left ideal. We describe in…
The algebraic method provides useful techniques to identify models in designs and to understand aliasing of polynomial models. The present note surveys the topic of Gr\"obner bases in experimental design and then describes the notion of…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded by the dimension. Combining Orlin's primal-based modification…
We present a method for the solution of polynomial equations. We do not intend to present one more method among several others, because today there are many excellent methods. Our main aim is educational. Here we attempt to present a method…