Numerical Optimization and Scaling
Scaling can often have a significant influence on the performance of an optimization routine.
Currently there are no user-callable scaling routines in the NAG Libraries, but scaling can be performed automatically in routines which solve sparse LP, QP or NLP problems and in some dense solver routines. Such routines have an optional parameter "Scale Option" which can be set by the user; see individual routine documents for details.
For other optimization routines, problems with unusual or unbalanced scaling may cause difficulty and it is usually well worth the effort to consider transformation of variables, scaling the objective function and scaling the constraints. Advice on all three of these aspects is given in the E04 Chapter Introduction, under the heading 'Scaling'.
More extensive advice can be found in P E Gill, W Murray and M H Wright, Practical Optimization, Academic Press, 1981.