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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 (E04NKF and E04UGF in the Fortran Library) incorporate some automatic scaling based on a method due to Fourier. The default scaling can be altered by using optional parameters ('Scale Option' and 'Scale Tolerance' in Fortran Library).

For other optimization routines, problems with unusual or unbalanced scaling may cause difficulty and it 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.

Tech Tip Update: Mark 21 of NAG's Fortran Library includes additional sparse optimisers with automatic scaling (E04NQF, E04VHF, E04WDF).

For specific technical advice in using NAG's products, please contact our technical experts.

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