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\title{\bf Quadratic Convergence of Potential-Reduction
Methods for Degenerate Problems}
\author{ Reha H. T\"{u}t\"{u}nc\"{u}
\thanks{Research supported in part by NSF through grant DMS-9706950 
and the Center for Nonlinear Analysis, and a Faculty Development 
Grant from Carnegie Mellon University.}\\
Department of Mathematical Sciences\\ Carnegie Mellon University\\
        Pittsburgh, PA 15213\\ {\tt reha+@andrew.cmu.edu}}
\date{December 2, 1998}

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\begin{abstract}
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Global and local convergence properties of a primal-dual interior-point
\textit{pure} potential-reduction algorithm for linear 
programming problems is analyzed. 
This algorithm is a primal-dual variant of the Iri-Imai method
and uses modified Newton search directions to 
minimize the Tanabe-Todd-Ye (TTY) potential function. 
A polynomial time complexity for the method is demonstrated.
Furthermore, this method is shown to have a unique accumulation 
point even for degenerate problems and to have Q-quadratic convergence
to this point by an appropriate choice of the step-sizes.
This is, to the best of our knowledge,
the first superlinear convergence result on degenerate
linear programs for primal-dual interior-point
algorithms that do not follow the central path.

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{\bf Key words: }
linear programming, potential functions, quadratic convergence, degeneracy 

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{\bf AMS subject classification: }90C05
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