Update to PositionBook Chart - Revised Optimisation Method

Just over a year ago I previewed a new chart type which I called a "PositionBook Chart" and gave examples in this post and this one. These first examples were based on an optimisation routine over 6 variables using Octave's fminunc function, an unconstrained minimisation routine. However, I was not 100% convinced that the model I was using for the loss/cost function was realistic, and so since the above posts I have been further testing different models to see if I could come up with a more satisfactory model and optimisation routine. The comparison between the original model and the better, newer model I have selected is indicated in the following animated GIF, which shows the last few day's action in the GBPUSD forex pair. 

The old model is figure(200), with the darker blue "blob" of positions accumulated at the lower, beginning of the chart, and the newer model, figure(900), shows accumulation throughout the uptrend. The reasons I prefer this newer model are:

• 4 of the 6 variables mentioned above (longs above and below price bar range, and shorts above and below price bar range) are theoretically linked to each other to preserve their mutual relationships and jointly minimised over a single input to the loss/cost function, which has a bounded upper and lower limit. This means I can use Octave's fminbnd function instead of fminunc. The minimisation objective is the minimum absolute change in positions outside the price bar range, which has a real world relevance as compared to the mean squared error of the fminunc cost function.
• because fminunc is "unconstrained" occasionally it would converge to unrealistic solutions with respect to position changes outside the price bar range. This does not happen with the new routine.
• once the results of fminbnd are obtained, it is possible to mathematically calculate the position changes within the price bar range exactly, without needing to resort to any optimisation routine. This gives a zero error for the change which is arguably the most important.
• the results from the new routine seem to be more stable in that indicators I am trying to create from them are noticeably less erratic and confusing than those created from fminunc results.
• finally, fminbnd over 1 variable is much quicker to converge than fminunc over 6 variables.
  

The second last mentioned point, derived indicators, will be the subject of my next post.