On the Convergence of the Iteration Sequence in Primal-Dual Interior-Point Methods

Abstract

Recently, numerous research efforts, most of them concerned with superlinear convergence of the duality gap sequence to zero in the Kojima-Mizuno-Yoshise primal-dual interior-point method for linear programming, have as a primary assumption the convergence of the iteration sequence. Yet, except for the case of nondegeneracy (uniqueness of solution), the convergence of the iteration sequence has been an important open question now for some time. In this work we demonstrate that for general problems, under slightly stronger assumptions than those needed for superlinear convergence of the duality gap sequence (except of course the assumption that the iteration sequence converges), the iteration sequence converges. Hence, we have not only established convergence of the iteration sequence for an important class of problems, but have demonstrated that the assumption that the iteration sequence converges is redundant in many of the above mentioned works.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1993
Accession Number
ADA452704

Entities

People

  • Richard A. Tapia
  • Yin Zhang
  • Yinyu Ye

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Convergence
  • Information Operations
  • Iterations
  • Linear Programming
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Operations Research