[ADMB Users] When and how to use set_scalefactor()?

[Shanae Allen - NOAA Affiliate]

Hi ADMB users!

I'm trying to understand when and how to scale parameters. The likelihood surface for the problem I'm working on is a narrow, curved valley (when varying the two most sensitive parameters), leading to high gradient components and non positive definite Hessians for some simulated data sets and starting values. According to Nocedal and Wright (1999), when the likelihood function is highly sensitive to a given parameter (x), you should set the scaling factor (d) to some large number such that a new parameter z is equal to x/d.
 
I'd like to use the built-in function in ADMB, set_scalefactor(s), but I'm unsure of how it treats the scaling factor. The ADMB site (http://www.admb-project.org/examples/function-minimization/parameter-scaling) suggests the new parameter z is equal to s*x, thus s=1/d. However, for my problem I obtain much better convergence when s is large (thus d is close to zero), which makes me wonder how ADMB is treating the scaling factor and whether I'm using it appropriately. Any tips would be greatly appreciated!

Thanks!

Shanae Allen

Nocedal, J., & Wright, S. (1999). Numerical optimization. New York: Springer.

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Shanae Allen-Moran
National Marine Fisheries Service
110 Shaffer Rd.
Santa Cruz, CA 95060
Phone: (831) 420-3970
Email: shanae...@noaa.gov
Website: http://swfsc.noaa.gov/SalmonAssessment/