In this paper computational aspects of transformation methods are studied. Transformation methods, which include sequential unconstrained minimization techniques (SUMTs) and multiplier methods, are based on solving a sequence of unconstrained minimization problems. An efficient technique is given to compute gradients of the transformation function. An operations count is given to demonstrate savings of the suggested technique over two other techniques used in the literature. Computer programs implementing the use of this technique in SUMTs and multiplier algorithms are developed. Applications of these programs on a set of structural design problems are given. Multiplier methods are found to be very stable and reliable, even on some relatively difficult problems, and they perform better than SUMTs. Some ways of improving the efficiency of transformation methods are given, together with possible extensions of using the suggested approach to compute gradients of implicit functions.
All Science Journal Classification (ASJC) codes
- Aerospace Engineering