A recursive quadratic programming algorithm for semi-infinite optimization problems

1982 ◽  
Vol 8 (1) ◽  
pp. 325-349 ◽  
Author(s):  
E. Polak ◽  
A. L. Tits
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Recursive Quadratic Programming

An Investigation of Pshenichnyi’s Recursive Quadratic Programming Method for Engineering Optimization

1987 ◽  
Vol 109 (2) ◽  
pp. 248-253 ◽  
Author(s):  
G. A. Gabriele ◽  
T. J. Beltracchi
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Test Problems ◽  
Engineering Optimization ◽  
Active Set ◽  
Original Algorithm ◽  
Recursive Quadratic Programming ◽  
Modified Algorithm ◽  
Engineering Optimization Problems

This paper discusses Pshenichnyi’s recursive quadratic programming algorithm for use in engineering optimization problems. An evaluation of the original algorithm is offered and several modifications are presented. The modifications include; addition of a variable metric update of the Hessian, an improved active set criterion, direct inclusion of the variable bounds, a divergence control mechanism, and updating schemes for the algorithm parameters. Implementations of the original algorithm and the modified algorithm were tested against the Sandgren test set of 23 engineering optimization problems. The results indicate that the modified algorithm was able to solve 20 of the 23 test problems while the original algorithm solved only 11. The modified algorithm was more efficient than the original on all the test problems.

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.

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 1—Concepts and Definitions

1989 ◽  
Vol 111 (1) ◽  
pp. 124-129 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Optimization Techniques ◽  
Discrete Variables ◽  
Convergence Criteria ◽  
Recursive Quadratic Programming ◽  
Analytical Properties ◽  
Discrete Optimization Problems

Although a variety of algorithms for discrete nonlinear programming have been proposed, the solution of discrete optimization problems is far from mature compared to continuous optimization techniques. This paper focuses on the recursive quadratic programming strategy which has proven to be efficient and robust for continuous optimization. The procedure is adapted to consider a class of mixed discrete nonlinear programming problems and utilizes the analytical properties of functions and constraints. This first part of the paper considers definitions, concepts, and possible convergence criteria. Part II includes the development and testing of the algorithm.

scholarly journals An active set sequential quadratic programming algorithm for nonlinear optimisation

2006 ◽  
Vol 74 (1) ◽  
pp. 69-83
Author(s):  
Qing-Jie Hu ◽  
Yun-Hai Xiao ◽  
Y. Chen
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Least Square ◽  
Programming Algorithm ◽  
Active Set ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Sequential Quadratic Programming Algorithm

In this paper, we have proposed an active set feasible sequential quadratic programming algorithm for nonlinear inequality constraints optimization problems. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a reduced quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving a reduced least square problem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without strict complementarity.

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