Premium
A recursive quadratic programming method with active set strategy for optimal design
Author(s) -
Belegundu Ashok D.,
Arora Jasbir S.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200503
Subject(s) - maxima and minima , mathematical optimization , convergence (economics) , quadratic programming , sequential quadratic programming , computer science , set (abstract data type) , quadratic equation , constraint (computer aided design) , fortran , scale (ratio) , algorithm , mathematics , mathematical analysis , physics , geometry , quantum mechanics , programming language , economics , economic growth , operating system
Recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics. There are two recursive quadratic programming methods that have been published in the literature. One is by Han and the other is by Pshenichny, published in 1977 and 1970, respectively. The algorithm of Pshenichny had been undiscovered until now, and is examined here for the first time. It is found that the proof of global convergence by Han requires computing sensitivity coefficients (derivatives) of all constraint functions of the problem at every iteration. This is prohibitively expensive for large‐scale applications in optimal design. In contrast, Pshenichny has proved global convergence of his algorithm using only an active‐set strategy. This is clearly preferable for large‐scale applications. The method of Pshenichny has been coded into a FORTRAN program. Applications of this method to four example problems are presented. The method is found to be very reliable. However, the method is found to be very sensitive to local minima, i.e. it converges to a local minimum nearest to the starting design. Thus, for optimal design problems (which usually possess multiple local minima) it is suggested that Pshenichny's method be used as part of a hybrid method.