Browsing by Author "Ye, Y."

Now showing 1 - 3 of 3
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    A Quadratically Convergent O(sqrt{n}L)-Iteration Algorithm for Linear Programming
    (1991-08) Ye, Y.; Güller, O.; Tapia, R.A.; Zhang, Y.
    Recently, Ye et al. proposed a large step modification of the Mizuno-Todd-Ye predictor-corrector interior-point algorithm for linear programming. They demonstrated that the large-step algorithm maintains theO (sqrt{n}L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.
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    A Superlinearly Convergent O(sqrt{n}L)-Iteration Algorithm for Linear Programming
    (1991-07) Ye, Y.; Tapia, R.A.; Zhang, Y.
    In this note we consider a large step modification of the Mizuno-Todd-Ye O (sqrt{n}L) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modified algorithm maintains its O (sqrt{n}L)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate problems. To our knowledge, this is the first construction of a superlinearly convergent algorithm with O (sqrt{n}L)-iteration complexity.
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    On the Convergence of the Iteration Sequence in Primal-Dual Interior-Point Methods
    (1991-08) Tapia, R.A.; Zhang, Y.; Ye, Y.
    This research is concerned with the convergence of the iteration sequence generated by a primal-dual interior-point method for linear programming. It is known that this sequence converges when both the primal and the dual problems have unique solutions. However, convergence for general problems has been an open question now for quite some time. In this work we demonstrate that for general problems, under mild conditions, the iteration sequence converges.