Progress Update: Midterm Evaluation

Objective:

Adding functions to the Optim package for Octave using existing back-ends.

Expected deliverables before midterm:

• 'lsqnonlin' using 'nonlin_residmin'

Done in [1]. Differences in backends, nonlin_residmin uses "lm_svd" algorithm for optimization as currently the only backend. However, lsqnonlin in Matlab can choose between "trust-region-reflective" and "Levenberg-Marquardt" (LM) algorithms.

Another difference is in complex inputs. lm_svd does not support complex valued inputs whereas Matlab's LM algorithm can accept complex input arguments. One way of providing complex inputs to lsqnonlin in Octave is to split the real and imaginary parts into separate variables and running the optimization.  

• 'lsqcurvefit' using 'nonlin_curvefit', 'nonlin_residmin', or 'lsqnonlin'

Done in [2] using nonlin_curvefit. lsqcurvefit is very similar to lsqnonlin with only a few minor interface differences. lsqcurvefit explicitly takes independent variables and the observations as inputs while these values can be wrapped inside the objective function while using lsqnonlin. Additional bounds for the optimized parameters can be specified. 

• 'nlinfit' using 'leasqr',

I wrapped nlinfit on nonlin_curvefit and curvefit_stat as leasqr repeats the optimization to compute the additional statistics (Jacobian and Covariance matrix) while curvefit_stat saves this computation overhead. I have partially implemented nlinfit in [3] (It hasn't been thoroughly reviewed yet). Two missing features are: 1) Error models and Error parameters estimation, and 2) Robust Weight function. Meanwhile, no such functionality exists in the Octave's optimization backends for the missing features. My current implementation supports the input of scalar positive array of weights for robust regression.  

Since nlinfit is from the statistics toolbox of Matlab, it uses statset and statget to create and get options respectively. I created additional functions statset, statget and __all_stat_opts__ with minor changes to the code in optimset, optimget and __all_opts__.

• 'fmincon' using 'nonlin_min',

In progress [4].


Future goals:

1. Complete fmincon implementation.
2. Create solver specific options using optimoptions and desirably still be able to use optimget. 
3. Arranging lambda output for quadprog by wrapping it on __qp__ instead of qp.m
4. Test cases for all the implemented functions.

[1] https://github.com/AsmaAfzal/octave_workspace/blob/master/lsqnonlin.m

[2] https://github.com/AsmaAfzal/octave_workspace/blob/master/lsqcurvefit.m

[3] https://github.com/AsmaAfzal/octave_workspace/blob/master/nlinfit.m
[4] https://github.com/AsmaAfzal/octave_workspace/blob/master/fmincon.m