On the convergence properties of Hildreth's quadratic programming algorithm

1990 ◽  
Vol 47 (1-3) ◽  
pp. 37-51 ◽  
Author(s):  
Alfredo N. Iusem ◽  
Alvaro R. De Pierro
Keyword(s):  
Quadratic Programming ◽  
Programming Algorithm ◽  
Convergence Properties

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.

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