Tuesday, June 27, 2017

Who needs Cplex or Gurobi: solving LPs using LU

The strange notion that linear programming problems can be solved simply by applying an LU decomposition (not as part of the Simplex method but just LU) seems to take hold. The original idea is from (1) but now we also can use LU as a solver for “Fuzzy Linear Fractional Programming Problems” (2).


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I agree with the abstract: the proposed approach is simple.

References
  1. S.M.Chincole, A.P.Bhadane, LU Factorization Method To Solve Linear Programming Problem, International Journal of Emerging Technology and Advanced Engineering ,Volume 4, Issue 4, 176-180, http://www.ijetae.com/files/Volume4Issue4/IJETAE_0414_31.pdf. Warning: this method does not work except in some very special cases (e.g. all constraints binding in the optimal solution).
  2. S. Muruganandam and P. Ambika,  Solving Fuzzy Linear Fractional Programming Problem using LU Decomposition Method, Annals of Pure and Applied Mathematics, Vol. 13, No 1., 2017, pp 89-97.
  3. Solving LP by LU??, http://yetanothermathprogrammingconsultant.blogspot.com/2017/01/solving-lp-by-lu.html