A primal-dual simplex method for linear programs

Authors:
Norman D. Curet
Affiliations:
Department of Mathematics, University of Wisconsin-Stevens Point, Stevens Point, USA
Venue:
Operations Research Letters
Year:
1993

Citing 4
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Abstract

A primal-dual algorithm is developed that optimizes a dual program in concert with improving primal infeasibility. The key distinction from the classic primal-dual simplex method is that our algorithm uses a much smaller working basis to determine a dual ascent direction quickly. By maintaining partial primal feasibility while improving the dual objective, the number of infeasible constraints is monotonically reduced to zero. Finite convergence to an optimal primal-dual pair can then be shown in the same manner as the simplex method. Computational experience on large generalized network linear programs demonstrates the algorithm's promise.