Linear Programming Algorithms Using Least-Squares Method

dc.contributor.advisor Johnson, Ellis L.
dc.contributor.advisor Barnes, Earl R.
dc.contributor.author Kong, Seunghyun en_US
dc.contributor.committeeMember Sokol, Joel
dc.contributor.committeeMember Savelsbergh, Martin W. P.
dc.contributor.committeeMember Prasad Tetali
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2007-05-25T17:24:42Z
dc.date.available 2007-05-25T17:24:42Z
dc.date.issued 2007-04-04 en_US
dc.description.abstract This thesis is a computational study of recently developed algorithms which aim to overcome degeneracy in the simplex method. We study the following algorithms: the non-negative least squares algorithm, the least-squares primal-dual algorithm, the least-squares network flow algorithm, and the combined-objective least-squares algorithm. All of the four algorithms use least-squares measures to solve their subproblems, so they do not exhibit degeneracy. But they have never been efficiently implemented and thus their performance has also not been proved. In this research we implement these algorithms in an efficient manner and improve their performance compared to their preliminary results. For the non-negative least-squares algorithm, we develop the basis update technique and data structure that fit our purpose. In addition, we also develop a measure to help find a good ordering of columns and rows so that we have a sparse and concise representation of QR-factors. The least-squares primal-dual algorithm uses the non-negative least-squares problem as its subproblem, which minimizes infeasibility while satisfying dual feasibility and complementary slackness. The least-squares network flow algorithm is the least-squares primal-dual algorithm applied to min-cost network flow instances. The least-squares network flow algorithm can efficiently solve much bigger instances than the least-squares primal-dual algorithm. The combined-objective least-squares algorithm is the primal version of the least-squares primal-dual algorithm. Each subproblem tries to minimize true objective and infeasibility simultaneously so that optimality and primal feasibility can be obtained together. It uses a big-M to minimize the infeasibility. We developed the techniques to improve the convergence rates of each algorithm: the relaxation of complementary slackness condition, special pricing strategy, and dynamic-M value. Our computational results show that the least-squares primal-dual algorithm and the combined-objective least-squares algorithm perform better than the CPLEX Primal solver, but are slower than the CPLEX Dual solver. The least-squares network flow algorithm performs as fast as the CPLEX Network solver. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/14529
dc.publisher Georgia Institute of Technology en_US
dc.subject Network flow en_US
dc.subject Linear programming en_US
dc.subject Least squares en_US
dc.subject Primal-dual method en_US
dc.title Linear Programming Algorithms Using Least-Squares Method en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Johnson, Ellis L.
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
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relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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