Related papers: Reducing the size and number of linear programs in…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
In this paper, we study a general online linear programming problem whose formulation encompasses many practical dynamic resource allocation problems, including internet advertising display applications, revenue management, various routing,…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
In this paper we present a new efficient variant to compute strong Gr\"obner basis over quotients of principal ideal domains. We show an easy lifting process which allows us to reduce one computation over the quotient $R/nR$ to two…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…
In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law…
Solving zero-dimensional polynomial systems using Gr\"obner bases is usually done by, first, computing a Gr\"obner basis for the degree reverse lexicographic order, and next computing the lexicographic Gr\"obner basis with a change of order…
In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points.…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
In the computation of a Gr"obner basis using Buchberger's algorithm, a key issue for improving the efficiency is to produce techniques for avoiding as many unnecessary critical pairs as possible. A good solution would be to avoid _all_…
ABC algorithms involve a large number of simulations from the model of interest, which can be very computationally costly. This paper summarises the lazy ABC algorithm of Prangle (2015), which reduces the computational demand by abandoning…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a…
What can be (machine) learned about the complexity of Buchberger's algorithm? Given a system of polynomials, Buchberger's algorithm computes a Gr\"obner basis of the ideal these polynomials generate using an iterative procedure based on…
This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…