Issue: 2024/Vol.34/No.2, Pages 163-182
A STEEPEST FEASIBLE DIRECTION METHOD FOR LINEAR PROGRAMMING. DERIVATION AND EMBEDDING IN THE SIMPLEX METHOD
Biressaw C. Wolde
, Torbjörn Larsson 
Cite as: B. C. Wolde, T. Larsson. A steepest feasible direction method for linear programming. Derivation and embedding in the simplex method. Operations Research and Decisions 2024: 34(2), 163-182. DOI 10.37190/ord2402010
Abstract
A feasible direction method for linear programming has been proposed. The method is embedded in the framework of the simplex method, even though it works with non-edge feasible directions. The direction used is the steepest in the space of all variables or an approximation thereof, and it is found by solving a strictly convex quadratic program in the space of the nonbasic variables. Further, this program guarantees the feasibility of the direction even in the case of degeneracy. To remain within the simplex framework, the direction is represented by an auxiliary, or external, nonbasic column, which is a nonnegative linear combination of original nonbasic columns. We have made an experimental evaluation of the suggested method on both nondegenerate and highly degenerate problem instances. The overall results are very promising for continued research along this line, especially concerning various computational strategies that can be applied when the method is implemented.
Keywords: linear programming, simplex method, steepest edge, feasible direction, external pivoting
Received: 22 December 2022 Accepted: 5 April 2024
Published online: 8 July 2024