A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

[+] Author and Article Information
T. J. Beltracchi

Performance Analysis Department, The Aerospace Corporation, P.O. Box 92957, Los Angeles, CA 90009-2957

G. A. Gabriele

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180

J. Mech. Des 113(3), 280-285 (Sep 01, 1991) (6 pages) doi:10.1115/1.2912780 History: Received November 01, 1989; Online June 02, 2008


The Recursive Quadratic Programming (RQP) method has become known as one of the most effective and efficient algorithms for solving engineering optimization problems. The RQP method uses variable metric updates to build approximations of the Hessian of the Lagrangian. If the approximation of the Hessian of the Lagrangian converges to the true Hessian of the Lagrangian, then the RQP method converges quadratically. The choice of a variable metric update has a direct effect on the convergence of the Hessian approximation. Most of the research performed with the RQP method uses some modification of the Broyden-Fletcher-Shanno (BFS) variable metric update. This paper describes a hybrid variable metric update that yields good approximations to the Hessian of the Lagrangian. The hybrid update combines the best features of the Symmetric Rank One and BFS updates, but is less sensitive to inexact line searches than the BFS update, and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is unaffected by the new update but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions obtained with the RQP method, and more importantly, provide more reliable information for post optimality analyses, such as parameter sensitivity studies.

Copyright © 1991 by The American Society of Mechanical Engineers
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