2012/06/19 by Deepak Ponvel Chermakani, Chermakani, Deepak Ponvel
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #Computational Complexity (cs.CC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1206.4236
openalex publication_date 2012/06/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a polynomial-time algorithm that obtains a set of Asymptotic Linear Programs (ALPs) from a given linear system S, such that one of these ALPs admits a feasible solution if and only if S admits a feasible solution. We also show how to use the same algorithm to determine whether or not S admits a non-trivial solution for any desired subset of its variables. S is allowed to consist of linear constraints over real variables with integer coefficients, where each constraint has either a lesser-than-or-equal-to, or a lesser-than, or a not-equal-to relational operator. Each constraint of the obtained ALPs has a lesser-than-or-equal-to relational operator, and the coefficients of its variables vary linearly with respect to the time parameter that tends to positive infinity.