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Limiting behavior of the affine scaling continuous trajectories for linear programming problems. (English) Zbl 0719.90044
The authors discuss the limiting behaviour of the continuous trajectories of the primal affine scaling (PAS) algorithm given by E. R. Barnes [Math. Program. 36, 174-182 (1986; Zbl 0626.90052)] and others, the dual affine scaling (DAS) algorithm given by the first author, M. Resende, G. Veiga and N. Karmarkar [ibid., Ser. A 44, No.3, 297- 335 (1989; Zbl 0682.90061)] and the primal-dual affine scaling (PDAS) algorithm introduced by the authors and M. Resende [Math. Oper. Res. 15, No.2, 191-214 (1990; Zbl 0714.90060)].
In this paper they present a weighted PAS algorithm and characterize its trajectories as solutions to a logarithmic barrier family of problems. The authors present several results on PAS, DAS and PDAS trajectories and claim to extend the results already obtained by N. Megiddo and M. Shub [ibid. 14, No.1, 97-146 (1989; Zbl 0675.90061)] and others about the limiting behaviour of PAS and PDAS trajectories. It is mentioned that their approach does not require the non-degeneracy assumption.
Reviewer: R.N.Kaul (Delhi)

90C05 Linear programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
Full Text: DOI
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