I wrote this post and am also happy to comment. Hopefully we'll be following this up soon with a post on treating robustness and cost simultaneously in a multicriteria setting. Also, special thanks again to Devon Sigler at the University of Colorado Denver for his help editing this post.
For anyone looking for a free optimization tool in python, sypy.opimize is easy to use.<p>Eg if I have a complicated function revenue([A,B,C,D])<p>I can define obj([A,B,C,D]) = -1* revenue([A,B,C,D])<p>and use:<p><pre><code> >>>import numpy as np
>>>from scipy.optimize import minimize
>>>X0 = np.array([1.5, 0.7, 1.2, 100])
>>>options={'xtol': 1e-4, 'disp': True})
>>>X* = minimize(obj, x0, method='nelder-mead', options)
</code></pre>
<a href="http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html" rel="nofollow">http://docs.scipy.org/doc/scipy/reference/tutorial/optimize....</a>
I'm one of the co-founders of SigOpt (YC W15) and am happy to answer any questions about SigOpt or the methods we apply.<p>More info on our research (and examples) can be found at <a href="https://sigopt.com/research" rel="nofollow">https://sigopt.com/research</a>
> The reason this is a more complicated situation is that an ordering of vectors in RkRk does not exist... how would one order the vectors u = (1,2,3), v = (2,1,3), w = (3,2,1)?<p>It seems straightforward to order those vectors by first comparing the first component, then the second, then the third. The result is u,v,w. It's as if you wanted to sort a multi-column report in Excel. What am I missing?
Here is a much simpler approach that works for many problems: minimize the distance to a desired multi-variate state.<p><a href="https://medium.com/@justchap/using-the-pythagorean-theorem-to-model-complicated-goals-in-machine-learning-b85f04b34ad4#.9tajh1t0l" rel="nofollow">https://medium.com/@justchap/using-the-pythagorean-theorem-t...</a>