A Note on a New Method Regular Solution of for Achieving an Initial a Linear Program
Abstract：Linear optimization has been widely used in the various areas of economics and management. In the case of filling the basic variables with negative values in solving a linear programming problem, Liang presented a new method for achieving an initial regular solution to the problem. This paper further discusses the essence of the method and finds out that the method consists of two phases. In phase 1, a nonnegative right-hand side vector is introduced to construct an auxiliary problem, which can generate a regular solution （if any） to the original problem by the primal simplex algorithm. Phase 2 applies the dual simplex algorithm to obtain the optimal solution （if any） starting from the regular solution. Furthermore, a numerical test on some large-scale instances from NETLIB is performed, and the results show that the method needs a great computational effort. Therefore, the paper presents an improvement of the method.
Keywords：linear programmingbasic feasible solutioninitial regular solutionsimplex algorithmdual simplex algorithm
Publication Date：2012-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：4( 1-4 )