Recursive quadratic programming methods based on the augmented lagrangian

1987 ◽  
pp. 21-41 ◽  
Author(s):  
M. C. Bartholomew-Biggs
Keyword(s):  
Quadratic Programming ◽  
Augmented Lagrangian ◽  
Recursive Quadratic Programming

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 2—Algorithm and Results

1989 ◽  
Vol 111 (1) ◽  
pp. 130-136 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Performance Comparison ◽  
Programming Algorithm ◽  
Discrete Variables ◽  
Contour Analysis ◽  
Recursive Quadratic Programming ◽  
Analysis Technique ◽  
Rank One ◽  
Symmetric Rank One ◽  
Monotonicity Analysis

A discrete recursive quadratic programming algorithm is developed for a class of mixed discrete constrained nonlinear programming (MDCNP) problems. The symmetric rank one (SR1) Hessian update formula is used to generate second order information. Also, strategies, such as the watchdog technique (WT), the monotonicity analysis technique (MA), the contour analysis technique (CA), and the restoration of feasibility have been considered. Heuristic aspects of handling discrete variables are treated via the concepts and convergence discussions of Part I. This paper summarizes the details of the algorithm and its implementation. Test results for 25 different problems are presented to allow evaluation of the approach and provide a basis for performance comparison. The results show that the suggested method is a promising one, efficient and robust for the MDCNP problem.

A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

1991 ◽  
Vol 113 (3) ◽  
pp. 280-285 ◽  
Author(s):  
T. J. Beltracchi ◽  
G. A. Gabriele
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Variable Metric ◽  
Hybrid Variable ◽  
Recursive Quadratic Programming ◽  
Line Searches ◽  
Inexact Line Searches ◽  
Rank One ◽  
Symmetric Rank One ◽  
Quadratic Programming Method

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.

Constrained Load Flow Using Recursive Quadratic Programming

1987 ◽  
Vol PER-7 (2) ◽  
pp. 24-25
Author(s):  
K. Aoki ◽  
A. Nishikori ◽  
R. Yokoyama
Keyword(s):  
Quadratic Programming ◽  
Load Flow ◽  
Recursive Quadratic Programming

Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming

1993 ◽  
Vol 115 (3) ◽  
pp. 405-410 ◽  
Author(s):  
G. R. Eisler ◽  
R. D. Robinett ◽  
D. J. Segalman ◽  
J. D. Feddema
Keyword(s):  
Quadratic Programming ◽  
Horizontal Plane ◽  
Tracking Error ◽  
Flexible Manipulator ◽  
Joint System ◽  
Recursive Quadratic Programming ◽  
Straight Line ◽  
Tip Position ◽  
The Impact ◽  
Structural Mode

The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.

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