Tech Tip: Scaling and Optimization
Scaling can often have a significant influence on the performance of an optimization routine. Routines for solving sparse LP, QP and nonlinear problems (E04NQF and E04VHF in the Fortran Library, e04nqc and e04vhc in the C Library, and similar names in other libraries) incorporate some automatic scaling based on a method due to Fourier. The default scaling can be altered by using optional parameters with names like 'Scale Option' and 'Scale Tolerance'.
For other optimization routines, problems with unusual or unbalanced scaling may cause difficulty and it's usually well worth the effort to consider transformation of variables, scaling the objective function and scaling of constraints. Advice on all three of these aspects is given in the E04 Chapter Introduction [pdf], 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.
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