[图书][B] Triangulations: structures for algorithms and applications

J De Loera, J Rambau, F Santos - 2010 - books.google.com
Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

[图书][B] Polytopes, rings, and K-theory

W Bruns, J Gubeladze - 2009 - books.google.com
Page 1 WINFRIED BRUNS JOSEPH GUBELADZE Polytopes, Rings, and K-Theory Springer
Springer Monographs in Mathematics Page 2 Springer Monographs in Mathematics For further …

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

J De Loera, X Goaoc, F Meunier, N Mustafa - Bulletin of the American …, 2019 - ams.org
We discuss five fundamental results of discrete mathematics: the lemmas of Sperner and
Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg …

[PDF][PDF] Nonlinear discrete optimization

S Onn - Zurich Lectures in Advanced Mathematics, European …, 2010 - pi.math.cornell.edu
Nonlinear Discrete Optimization Page 1 Shmuel Onn Technion – Israel Institute of Technology
http://ie.technion.ac.il/~onn Nonlinear Discrete Optimization Based on several papers joint with …

Carathéodory bounds for integer cones

F Eisenbrand, G Shmonin - Operations Research Letters, 2006 - Elsevier
Carathéodory bounds for integer cones - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue …

Sparse solutions of linear diophantine equations

I Aliev, JA De Loera, T Oertel, C O'Neill - SIAM Journal on Applied Algebra and …, 2017 - SIAM
We present structural results on solutions to the Diophantine system Ay=b, y∈Z^t_≥0 that
have the smallest number of nonzero entries. Our tools are algebraic and number theoretic …

Improving proximity bounds using sparsity

J Lee, J Paat, I Stallknecht, L Xu - … ISCO 2020, Montreal, QC, Canada, May …, 2020 - Springer
We refer to the distance between optimal solutions of integer programs and their linear
relaxations as proximity. In 2018 Eisenbrand and Weismantel proved that proximity is …

[HTML][HTML] The power of pyramid decomposition in Normaliz

W Bruns, B Ichim, C Söger - Journal of Symbolic Computation, 2016 - Elsevier
We describe the use of pyramid decomposition in Normaliz, a software tool for the
computation of Hilbert bases and enumerative data of rational cones and affine monoids …

On augmentation algorithms for linear and integer-linear programming: From Edmonds--Karp to Bland and beyond

JA De Loera, R Hemmecke, J Lee - SIAM Journal on Optimization, 2015 - SIAM
Motivated by Bland's linear programming (LP) generalization of the renowned Edmonds--
Karp efficient refinement of the Ford--Fulkerson maximum flow algorithm, we analyze three …

Problems and algorithms for affine semigroups

W Bruns, J Gubeladze, NV Trung - arXiv preprint math/0101116, 2001 - arxiv.org
In this article we overview those aspects of the theory of affine semigroups and their
algebras that have been relevant for our own research, and pose several open problems …