Strategies for Creating Advanced Bases for Large-Scale Linear Programming Problems
Published Online:1 May 1998https://doi.org/10.1287/ijoc.10.2.248
References
- An Augmented Lagrangian Method for Linear Programming. (1985) . Working paper, presentation at the 12th International Mathematical Programming Symposium, Boston, MA Google Scholar
- A Standard Input Format for Multiperiod Stochastic Linear Programs, Mathematical Programming Society. Committee on Algorithms Newsletter (1987) 17 Google Scholar
- Implementing the Simplex Method: The Initial Basis. ORSA Journal on Computing (1992) 4 3 267 284 Link, Google Scholar
- , Orchard-Hays W. Crashing Techniques. Advanced Linear-Programming Computing Techniques (1968) (McGraw-Hill, New York) 131 139 Google Scholar
- Row Action Methods for Huge Sparse Systems and their Applications. SIAM Review (1981) 23 4 444 466 Crossref, Google Scholar
- Parallel Application of Block Iterative Methods in Medical Imaging and Radiation Therapy. Mathematical Programming (1988) 42 307 325 Crossref, Google Scholar
- Linear Programming (1983) (Freeman, New York) Google Scholar
- An Extension of Set Partitioning with Application to Scheduling Problems. European Journal of Operational Research (1985) 21 200 205 Crossref, Google Scholar
- A Collection of Scheduling Problems from the SUPERBUS Project (EU): Quality Assurance and Testing. (1996) . Technical report, TR/7/96, Department of Mathematics and Statistics, Brunel University, London Google Scholar
- A Structurally Stable Modification of Hellerman and Rarick's P 4 Algorithm for Reordering Unsymmetric Sparse Matrices. SIAM Journal on Numerical Analysis (1985) 22 369 385 Crossref, Google Scholar
- Iterative Algorithms for Large Partitioned Linear Systems with Application to Image Reconstruction. Linear Algebra and Applications (1987) 40 37 67 Crossref, Google Scholar
- FortMP Manual (1994) (Brunel University, London) . and Numerical Algorithms Group (NAG), Oxford, UK Google Scholar
- Steepest-Edge Simplex Algorithms for Linear Programming. Mathematical Programming (1993) 57 341 374 Crossref, Google Scholar
- Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society. Committee on Algorithms Newsletter (1985) 13 10 12 Google Scholar
- On the Finite Convergence of the Relaxation Method for Solving Systems of Inequalities. (1971) (Operation Research Center, Berkeley) . ORC 71-36, UCLA Google Scholar
- , Bunch J. , Rose D. Using the Steepest-Edge Simplex Algorithm to Solve Sparse Linear Programs. Sparse Matrix Computations (1976) (Academic Press, New York) 227 240 Crossref, Google Scholar
- Matrix Computation (1983) (North Oxford Academic, Oxford, UK) Google Scholar
- New Crash Procedures for Large Systems of Linear Constraints. Mathematical Programming (1989) 45 475 501 Crossref, Google Scholar
- Harwell Subroutine Library A Catalogue of Subroutines. (1988) (HMSO, London) Google Scholar
- Image Reconstruction Form Projections: The Fundamentals of Computational Tomography (1990) (Academic Press, New York) Google Scholar
- A Review of Models and Solution Methods in Positron Emission Tomography (PET) Image Reconstruction. (1995) . Technical report, TR/10(9)/95, Brunel University, London Google Scholar
- Angenaherte Auflösung von Systemen linearer Gleichungen. Bulletin de l'Academie Polonaise des Sciences Letters A (1937) 35 355 357 Google Scholar
- KRASH, An Adaptive Relaxation Method for Solving Linear Programs. (1986) . Department of Computer Science, University of Texas at Austin Google Scholar
- A New Polynomial Time Algorithm for Linear Programming. Combinatorica (1984) 4 375 395 Crossref, Google Scholar
- Iterative Solution of Linear Programs. SIAM Journal of Numerical Analysis (1981) 18 4 606 614 Crossref, Google Scholar
- The Elimination Form of the Inverse and Its Applications to Linear Programming. Management Science (1954) 3 255 269 Link, Google Scholar
- Adaptivity in Linear Programming, II (in Hungarian). Alkalmazott Matematikai Lapok (1981) 7 1 71 Google Scholar
- A general Phase-I Method in Linear Programming. European Journal of Operational Research (1986) 23 64 77 Crossref, Google Scholar
- A Three-Parameter-Arithmetic (TPA). (1989) . Working paper MO/85, Computer and Automation Institute (MTA SZTAKI), Budapest, Hungary Google Scholar
- MILP Linear Programming System. User's Guide for Version V3.40. (1990) . Computer and Automation Institute (MTA SZTAKI), Budapest, Hungary Google Scholar
- , Kleinschmidt P. , Bachem A. , Derigs U. , Fischer D. , Leopold-Wildburger U. , Möhring R. Finding Better Starting Bases for the Simplex Method. Operations Research Proceedings 1995 (1996) (Springer Verlag, Berlin, Heidelberg, New York) 7 12 Crossref, Google Scholar
- , Beasley J. Simplex Algorithms. Advances in Linear and Integer Programming (1996) (Oxford University Press, Oxford, UK) 1 46 Crossref, Google Scholar
- Modelling and Analysis of Multistage Stochastic Programming Problems: A Software Environment. European Journal of Operational Research (1997) 101 343 359 Crossref, Google Scholar
- , Kumar S. Alternative Methods for Representing the Inverse of Linear Programming Basis Matrices. Recent Developments in Mathematical Programming (1990) (Gordon and Breach, Reading, MA) 273 302 Google Scholar
- A Fortran Based Linear Programming System: FortLP (1990) . User Reference Manual, Version 3.1, Brunel University, Uxbridge, and NAG, Ltd, Oxford, UK Google Scholar
- Experimental Investigation of an Interior Search Method within a Simplex Framework. Communications of the ACM (1988) 31 12 1474 1482 Crossref, Google Scholar
- The Relaxation Method for Linear Inequalities. Canadian Journal of Mathematics (1954) 6 393 404 Crossref, Google Scholar
- MINOS 5.1 User's Guide. (1987) . Technical report SOL 83-20R, Stanford University, Stanford, California Google Scholar
- Advanced Linear-Programming Computing Techniques (1968) (McGraw-Hill, New York) Google Scholar
- Computing Sparse LU Factorizations for Large-Scale Linear Programming Bases. ORSA Journal on Computing (1990) 2 4 325 335 Link, Google Scholar
- The Composite Simplex Algorithm. SIAM Review (1965) 7 42 54 Crossref, Google Scholar

