Implementation of Presolving and Interior-Point Algorithm for Linear & Mixed Integer Programming: SOFTWARE

References

[1] Brearley A L, Mitra G, Williams H P. Analysis of mathematical programming problems prior to applying the simplex algorithm. ORSA Journal on Computing, 1994, 6(1): 15–22.10.1007/BF01580428Suche in Google Scholar

[2] Gondzio J. Presolve analysis of linear programs prior to applying an interior point method. Informs Journal on Computing, 1994, 13(1): 73–91.10.1287/ijoc.9.1.73Suche in Google Scholar

[3] Gal T. Weakly redundant constraints and their impact on post optimal analysis. European Journal of Operational Research, 1979, 60: 315–326.10.1016/0377-2217(92)90083-LSuche in Google Scholar

[4] Caron R J, McDonald J F, and Ponic C M. A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary. Journal of Optimization Theory and Application, 1989, 62(2): 225–237.10.1007/BF00941055Suche in Google Scholar

[5] Telgan J. Identifying redundant constraints and implicit equalities in system of linear constraints. Management Science, 1983, 29(10): 1209–1222.10.1287/mnsc.29.10.1209Suche in Google Scholar

[6] Paulraj S, Sumathi A. A comparative study of redundant constraints identification methods in linear programming problems. Mathematical Problems in Engineering, 2010(1): 242–256.10.1155/2010/723402Suche in Google Scholar

[7] Paulraj S, Sumathi M P. A new approach for selecting a constraint linear programming problems to identify the redundant constraints. International Journal of Scientifi & Engineering Research, 2012, 3(8): 1–4.Suche in Google Scholar

[8] Paulraj S, Chellappan C, Natesan T R. A heuristic approach for identification of redundant constraints in linear programming models. International Journal of Computer Mathematics, 2006, 83(8–9): 675–683.10.1080/00207160601014148Suche in Google Scholar

[9] Stojkovie N V, Stanimirovie P S. Two direct methods in linear programming. European Journal of Operational Research, 2001, 131(2): 417–439.10.1016/S0377-2217(00)00083-7Suche in Google Scholar

[10] Meszaros C S, Suhl U H. Advanced preprocessing techniques for linear and quadratic programming. OR Spectrum, 2003, 25: 575–595.10.1007/s00291-003-0130-xSuche in Google Scholar

[11] Adler I, Resende M G C, Verga G, et al. An implementation of Karmarkar’s algorithm for linear programming. Mathematical Programming, 1989, 44(3): 297–335.10.1007/BF01587095Suche in Google Scholar

[12] Chang S F, McCormick S T. A hierarchical algorithm for making sparse matrices sparser. Mathematical Programming, 1992, 56: 1–30.10.1007/BF01580890Suche in Google Scholar

[13] Adler I, karmarkar N, Resende M G C, et al. Data structure and programming techniques for implementation of Karmakr’s algorithm. ORSA Journal on Computing, 1989, 1(2): 84–106.10.1287/ijoc.1.2.84Suche in Google Scholar

[14] Lusting I J, Marsten R E, Shanno D F. Computational experience with a primal-dual interior point method for linear programming. Linear Algebra and Its Applications, 1991, 152: 191–222.10.1016/0024-3795(91)90275-2Suche in Google Scholar

[15] Brearley A L, Mitra G, and Williams H P. Analysis of mathematical programming problems prior to applying the simplex algorithm. Math Prog, 1975, 8: 54–83.10.1007/BF01580428Suche in Google Scholar

[16] Williams H. A reduction procedure for linear and integer programming models. Re-dundancy in Mathematical Programming. Volume 206 of Lecture Notes in Economics and Mathematicals Systems. Springer Berlin Heidelberg, 1983: 87–107.10.1007/978-3-642-45535-3_9Suche in Google Scholar

[17] Andersen E D, Andersen K D. Presolving in linear programming. Mathematical Programming, 1983, 71: 87–107.10.1007/BF01586000Suche in Google Scholar

[18] Crowder H, Johnson E L, Padeberg M W. Solving large-Scale zero-one linear programming problems. Operations Research, 1983, 31: 803–834.10.1287/opre.31.5.803Suche in Google Scholar

[19] Hoffman K L, Padberg M. Improving LP-representation of zero-one linear programs for branch-and-cut. ORSA Journal on Computing, 1991, 3: 121–134.10.1287/ijoc.3.2.121Suche in Google Scholar

[20] Williams H P. The elimination of integer variables. The Journal of the Operational Research Society, 1992, 43(5): 387–393.10.1057/jors.1992.65Suche in Google Scholar

[21] Savelsbergh M W P. Preprocessing and probing techniques for mixed integer programming problems. OPRSA Journal on Computing, 1994, 6(4): 445–454.10.1287/ijoc.6.4.445Suche in Google Scholar

[22] Achterberg T. Constraint integer programming. Technical University of Berlin, 2007.Suche in Google Scholar

[23] Bixby R E, Rothberg E. Progress in computational mixed integer programming –- A look back from the other side of the tipping point. Annals of Operations Research, 2007, 149: 37–41.10.1007/s10479-006-0091-ySuche in Google Scholar

[24] Gamrath G, Koch T, Martin A, et al. Progress in presolving for mixed integer programming. Mathematical Programming Computation, 2015, 7: 367–398.10.1007/s12532-015-0083-5Suche in Google Scholar

[25] Mahajan A. Presolving mixed-integer linear programs. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439, 2010.10.1002/9780470400531.eorms0437Suche in Google Scholar

[26] Sadhana V V. Efficient presolving in linear programming. University of Florida, 2002.Suche in Google Scholar