A recursive quadratic programming algorithm that uses a new nondifferentiable penalty functions

1994 ◽  
Vol 9 (1) ◽  
pp. 95-103
Author(s):  
Yang Boting ◽  
Zhang Kecun
Keyword(s):  
Quadratic Programming ◽  
Penalty Functions ◽  
Programming Algorithm ◽  
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.

Optimization With Discrete Variables via Recursive Quadratic Programming: Part II — Algorithm and Results

1987 ◽  
Author(s):  
J. C. Cha ◽  
R. W. Wayne
Keyword(s):  
Quadratic Programming ◽  
Performance Comparison ◽  
Programming Algorithm ◽  
Discrete Variables ◽  
Contour Analysis ◽  
Recursive Quadratic Programming ◽  
Analysis Technique ◽  
Rank One ◽  
Symmetric Rank One ◽  
Monotonicity Analysis

Abstract A discrete recursive quadratic programming algorithm is developed for mixed discrete constrained nonlinear progrmming (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 strategy 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 this 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.

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.

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