Experiments with UNA for solving linear constraints in real variables

Linear constraints arise in formulation of several computationally challenging problems such as weather modeling, underground water modeling, air pollution modeling etc. The constraints may correspond to multiple observations that place upper or lower bounds on linear combinations of variables. Computing a feasible solution or solving these inequalities in least squares sense is a fundamental problem in many applications.In this paper, we present a strikingly simple numerical algorithm called UNA (Unified Numerical Approach) that computes a feasible solution of linear inequalities or solves them in a least squares sense in case they are inconsistent. We compare the performance of UNA with Bramley-Winnicka algorithm, which is the best known algorithm to solve linear inequalities in a least squares sense. We also give experimental performance comparison of UNA with commercial linear programming based packages XA and CPLEX. Our experiments show that UNA algorithm is faster than Bramley-Winnicka algorithm for solving large constraint sets in least squares sense. Our experiments also show that for large constraint sets although CPLEX performs better than UNA, UNA performs far better than XA. In addition, the UNA algorithm is so simple that its implementation in C programming language is only 170 lines of code and its implementation using Matlab is 80 lines of matlab script. Our results show that in-spite of its simplicity, it is a powerful algorithm for solving linear inequalities in real variables.