Interior-Point Methods for Lagrangian Duals of Semidefinite Programs

Mituhiro Fukuda and Masakazu Kojima

This paper proposes a new primal-dual predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguishing features of the method are full use of the BFGS quasi-Newton method in the corrector procedure and an application of the conjugate gradient method with an effective preconditioning matrix induced from the BFGS quasi-Newton method in the predictor procedure. Some preliminary numerical results are presented.

Research Report B-365, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, December 2000