A Generic Path-Following Algorithm with a Sliding Constraint and its Application to Linear Programming and the Computation of Analytic Centers
Cahiers de recherche; 1996.08
|Abstract||We propose a generic path-following scheme which is essentially a method of centers that can be implemented with a variety of algorithms. The complexity estimate is computed on the sole assumption that a certain local quadratic convergence property holds, independently of the specific algorithmic procedure in use, primal, dual or primal-dual. We show convergence in iterations. We verify that the primal, dual and primal-dual algorithms satisfy the local quadratic convergence property. The method can be applied to solve the linear programming problem (with a feasible strat) and to compute the analytic center of bounded polytope. The generic path-following scheme easily extends to the logarihmic barrier approach|
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|VIAL, Jean-Philippe. A Generic Path-Following Algorithm with a Sliding Constraint and its Application to Linear Programming and the Computation of Analytic Centers. 1996 https://archive-ouverte.unige.ch/unige:5952|