A new polynomial-time algorithm for linear programming
Combinatorica
An improved intial basis for the simplex algorithm
Computers and Operations Research
An Improved Simplex-Genetic Method to Solve Hard Linear Programming Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
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A feasible direction method for solving Linear Programming (LP) problems, followed by a procedure for purifying a non-basic solution to an improved extreme point solution have been embedded within an otherwise simplex based optimizer. The algorithm is designed to be hybrid in nature and exploits many aspects of sparse matrix and revised simplex technology. The interior search step terminates at a boundary point which is usually non-basic. This is followed by a series of minor pivotal steps which lead to a basic feasible solution with a superior objective function value. It is concluded that the procedures discussed in this article are likely to have three possible applications, which are(i) improving a non-basic feasible solution to a superior extreme point solution,(ii) an improved starting point for the revised simplex method, and(iii) an efficient implementation of the multiple price strategy of the revised simplex method.