Closure to “Discussion of ‘An Investigation of Pshenichnyi’s Recursive Quadratic Programming Method for Engineering Optimization’” (1987, ASME J. Mech. Transm. Autom. Des., 109, pp. 254–256)

1987 ◽  
Vol 109 (2) ◽  
pp. 256-256
Author(s):  
G. A. Gabriele ◽  
T. J. Beltracchi
Keyword(s):  
Quadratic Programming ◽  
Programming Method ◽  
Engineering Optimization ◽  
Recursive Quadratic Programming ◽  
Quadratic Programming Method

A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

1989 ◽  
Author(s):  
T. J. Beltracchi ◽  
G. A. Gabriele
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Engineering Optimization ◽  
Variable Metric ◽  
Hybrid Variable ◽  
Recursive Quadratic Programming ◽  
Rank One ◽  
Sensitivity Studies ◽  
Symmetric Rank One ◽  
Quadratic Programming Method

Abstract The Recursive Quadratic Programming (RQP) method has been shown to be 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 convergence of the Hessian approximation is affected by the choice of the variable metric update. Most of the research that has been performed with the RQP method uses the Broyden Fletcher Shanno (BFS) or Symmetric Rank One (SR1) variable metric update. The SR1 update has been shown to yield better estimates of the Hessian of the Lagrangian than those found when the BFS update is used, though there are cases where the SR1 update becomes unstable. This paper describes a hybrid variable metric update that is shown to yield good approximations of the Hessian of the Lagrangian. The hybrid update combines the best features of the SRI and BFS updates and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is not affected by the new update, but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions and provide more reliable information for post optimality analyses, such as parameter sensitivity studies.

scholarly journals Optimal use of quadratic programming method for alignment of geodesic networks

2019 ◽  
Vol 15 (2) ◽  
pp. 38-42
Author(s):  
O.S. Goncharenko ◽  
V.N. Gladilin ◽  
L. Šiaudinytė
Keyword(s):  
Quadratic Programming ◽  
Programming Method ◽  
Quadratic Programming Method
Sign in / Sign up

Export Citation Format

Share Document