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I need to use optimisation to solve for the variables in the following matrix:

figure 1.0

The yellow highlighted matrix contains all the variables I want to solve for.

Before for each case, the equations of motion were solved for each time point using an optimization approach that is based upon a cost function adapted from the work of Crowninshield & Brand [24] and Raikova [25]. The optimization was solved using the optimization toolbox of MATLAB (R2103a; The Mathworks, Inc, 2013):

Here is he cost function.

Figure 2.0

I realise all these matrices and equations will have variables you won't necessarily understand. However, my question is this- Is there an open source alternative for optimisation with similar functionality as fmincon? I am working on finding a faster alternative so speed is my priority.

This is for a student project. If I show my professor some tangible results in having been able to reduce the time taken for solving he will be quite happy. As far as I can understand he says the fmincon function on matlab is slow and inefficient.

Thanks!

Chenks
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    Should be marked as duplicate. Check out https://stackoverflow.com/questions/6403282/non-linear-least-squares-optimization-library-for-c. Or this https://stackoverflow.com/questions/5439321/implementation-of-matlabs-fmincon-function-in-c?rq=1. – bnaecker Mar 12 '16 at 16:20
  • May be you can elaborate why you consider fmincon to be slow (compared to what?). fmincon has quite a few knobs you can tune (e.g. algorithm). Furthermore make sure you pass on analytic gradients instead of letting the algorithm do finite differences. – Erwin Kalvelagen Mar 13 '16 at 17:04

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