Lagrangian Dual Interior-Point Methods for Semidefinite Programs

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. Key words. semidefinite program, primal-dual interior-point method, predictor-corrector method, Lagrangian dual, BFGS quasi-Newton method, conjugate gradient method AMS subject classifications. 90C22, 90C51, 90C53, 65F10, 49N15, 49M29

• Type: Journal
• Year: 2002
• Where: SIAMJO
• Authors: Mituhiro Fukuda, Masakazu Kojima, Masayuki Shida
• Keywords: Gradient Method, Interior-point Method, Predictor-corrector Interior-point Method, SIAMJO 2002