Linear programming: active set analysis and computer programs
Linear programming: active set analysis and computer programs
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In this paper, generalized linear programming (GLP) is treated as a generator of feasible directions for the associated Lagrangian dual problem. In particular, we examine the ascent property of d"G"L"P which is defined to be the difference of two successive dual iterates generated by GLP. It is shown that d"G"L"P always ascends the dual function, L, at the points where L is differentiable. At nondifferentiable points, the choice of column entering the master problem is not unique and an arbitrary choice can produce a nonascent direction. However by appropriate choice of entering column(s), d"G"L"P will be an ascent direction. Computational results on random problems indicate that adding line searches along d"G"L"P directions can improve the performance of GLP.