Originally posted by: Uonly

Hi community,

I have a problem that produces inaccurate dual solutions. I could either tune Markowitz tolerance or Numerical Emphasis to get accurate solutions.

Can anyone give some insight of the differences between these two approaches? it seems Numerical Emphasis is more generic and has covered Markowtiz tolerances? In another word, what does numerical emphasis do after we turn it on? more aggressive scaling? tighter internal tolerances or also increase Markowitz tolerance to some high value? Will it hurt if I set Markowitz tolerance to 0.99999 and keep numerical emphasis true at the same time?

Thanks again.

Sincerely,

Uonly

Originally posted by: BoJensen

By inaccurate dual solutions I assume you checked the solution quality, what range of inaccuracy do you see ?

Often the inaccurate solutions is a result of numerical instabil data i.e very large (or very small) objective, large bounds etc. Please check your model for such issues and improve them if possible.

Then I recommend :

1) The numerical emphasis should be turned on (does several things internally to improve numerical accuracy)

2) Set scaling parameter to aggressive scaling

3) Set Markowitz tolerance to a high number like 0.9

Regarding Markowitz tolerance, then this is a parameter which controls the tradeoff between fill and numerical stability in the LU factorization module. In general a higher number means more focus on choosing a numerical better pivot element, but it also creates more fill in.