Lagrangian dual interior-point methods for semidefinite programs

Mituhiro Fukuda, Masakazu Kojima, and Masayuki Shida

This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished 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 reported.

Research Report B-369, Dept. Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8552 Japan, March 2001.