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On the convergence behavior of trajectories for linear programming. (English) Zbl 0725.90060
Mathematical developments arising from linear programming, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 114, 161-187 (1990).
Summary: [For the entire collection see Zbl 0722.00047.]
The convergence behavior of center trajectories arising from the use of the logarithmic barrier function in linear programming is examined based on the concept of analytic center of a system of linear constraints. Main results are the convergence of A-trajectories to g-centers of the optimal face and the convergence of their tangential directions. Both results hold in the presence of primal and dual degeneracies, g-center varieties are introduced extending the concept of analytic g-centers.

MSC:
90C05 Linear programming
65K05 Numerical mathematical programming methods
90-08 Computational methods for problems pertaining to operations research and mathematical programming