ALPO: Another Linear Program Optimizer

This paper describes an implementation ofthe one-phase primal-dual path-following algorithm for solving linear programming problems. The design is intended to be simple, portable and robust. These design goals are achieved without sacrificing stateofthe-art performance. We give a rather complete description of the algorithm and the implementation. Computational results obtained for the NET LIB suite of problems run on a Silicon Graphics workstation are also presented. This paper documents a new linear program solver called ALPO. ALPO is written entirely in C and can easily be ported to a variety of computing environments. ALPO is intended to be simple, portable and robust. It also turns out to be efficient (see Section 3). ALPO is easy to use. Other than specifying a problem and the level of precision desired in the answer, there are no user adjustable parameters. ALPO can be run as a stand-alone program (called alpo), or it can be accessed from either C or FORTRAN as a small library of functions. If it is executed from the command line, it takes its input from industry-standard MPS format files. A function called optlp is the heart ofthe system. It uses the one-phase primal-dual pathfollowing algorithm to solve problems presented in standard form (all MPS format problems are first converted to standard form). This algorithm is one of the recently discovered interior point methods for linear programming that has appeared as a result of the intense research that has ensued from the publication of N. Karmarkar's seminal paper [121. As its basic engine, optlp uses Cholesky factorization routines (with a minimum-local-fill ordering heuristic) for solving symmetric nonnegative definite systems of equations. Whenever there was a choice between using a simple algorithm or a sophisticated one, we have opted for the simple algorithm. It is our belief that the performance penalty for such a compromise is generally modest (see Section 3). As a result the entire code, consisting of less than 1400 non-comment lines (about 2000 lines in total), is quite short and understandable. By way of comparison, just the data input routine in KORBX (kmps) has about 5000 lines. Since we are currently seeing so many rapid advances in our understanding of efficient interior point methods for mathematical programming, it would be very useful to have a platform from which different methods and new advances could be studied easily. ALPO is well suited for this purpose. As an example, ALPO was recently modified to solve separable quadratic programming problems. This modification took less than a day to design, implement and debug. The one-phase primal-dual path-following algorithm IS described m the next section.