Integer Programming Subject to Monomial Constraints

Abstract. We investigate integer programs containing monomial constraints of the type Q iI xi i = b. Due to the number-theoretic nature of these constraints, standard methods based on linear algebra cannot be applied directly. Instead, we present a reformulation resulting in integer programs with linear constraints and polynomial objective functions, using prime decompositions of the right hand sides b. Moreover, we show that minimizing a linear objective function with nonnegative coefficients over bivariate constraints is possible in polynomial time.

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Christoph Buchheim, Dennis Michaels, Robert Weismantel
• Keywords: Integer Programs, Linear Objective Function, Objective Function, SIAMJO 2010