2003/10/13 by Bernd Sturmfels, Sturmfels, Bernd
Computer Science · Mathematics · #90C10 #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #Constraint Satisfaction and Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Polynomial and algebraic computation #math.AC #math.OC #msc:90C10
paper · pdf · doi:10.48550/arxiv.math/0310194
15 pages
arxiv created 2003/10/13 · openalex publication_date 2003/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also consider parametric versions where the objective function and the right hand side are allowed to vary. The main emphasis is on Gröbner bases, rational generating functions, and how to use existing software packages. Concrete applications to problems in statistical modeling will be presented. These are the notes for a lecture to be given during the AMS Short Course, ``Trends in Optimization'', prior to the Joint Mathematics Meetings in Phoenix on January 5-6, 2004.