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On quadratic convergence of the $$O\left( {\sqrt {nL} } \right)$$ -iteration homogeneous and self‐duallinear programming algorithm

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  • F. Wu
  • S. Wu
  • Y. Ye

Abstract

In this paper, we show that Ye‐Todd‐Mizuno's O( $$\sqrt {nL} $$ ) ‐iteration homogeneous andself‐dual linear programming (LP) algorithm possesses quadratic convergence of the duality gap to zero. In the case of infeasibility, this shows that a homogenizing variable quadratically converges to zero (which proves that at least one of the primal and dual LP problems is infeasible) and implies that the iterates of the (original) LP variable quadratically diverge. Thus, we have established a complete asymptotic convergence result for interior‐point algorithms without any assumption on the LP problem. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • F. Wu & S. Wu & Y. Ye, 1999. "On quadratic convergence of the $$O\left( {\sqrt {nL} } \right)$$ -iteration homogeneous and self‐duallinear programming algorithm," Annals of Operations Research, Springer, vol. 87(0), pages 393-406, April.
    • Handle: RePEc:spr:annopr:v:87:y:1999:i:0:p:393-406:10.1023/a:1018905724427
    DOI: 10.1023/A:1018905724427
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