On the Convergence of Interior-Point Methods to the Center of the Solution Set in Linear Programming
RICE UNIV HOUSTON TX DEPT OF MATHEMATICAL SCIENCES
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The notion of the central path plays an important role in the convergence analysis of interior-point methods. Many interior-point algorithms have been developed based on the principle of following the central path, either closely or otherwise. However, whether such algorithms actually converge to the center of the solution set has remained an open question. In this paper, we demonstrate that under mild conditions, when the iteration sequence generated by a primal-dual interior-point method converges, it converges to the center of the solution set.
- Numerical Mathematics
- Operations Research