A First-order e-approximation algorithm for linear programs and a second-order implementation

Abstract

This article presents an algorithm that finds an e-feasible solution relatively to some constraints of a linear program. The algorithm is a first-order feasible directions method with constant stepsize that attempts to find the minimizer of an exponential penalty function. When embedded with bisection search, the algorithm allows for the approximated solution of linear programs. We present applications of this framework to set-partitioning problems and report some computational results with first-order and second-order implementations.