Lagrangian dual interior-point methods for semidefinite programs

Published: 2001/04/03, Updated: 2004/04/29

Convex Optimization, Second-Order Cone Programming, Semi-definite Programming bfgs quasi-newton method, central trajectory, conjugate gradient method, lagrangian dual, linear program over convex cones, predictor-corrector method, primal-dual interior-point method, second-order cone program, semidefinite programming Short URL: https://optimization-online.org/?p=8677

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.

Citation

SIAM Journal on Optimization Vol 12, No.4, 1007-1031 (2002).