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I am using MinBLEIC in AlgLib 3.9.0 to determine weights of N explanatory time series to best fit a single analyzed time series (all series are aligned in time). Each weight has to between 0 and 1, as set through N boundary constraints. All weights have to add up to 1 through a single linear constraint. The cost function being minimized is the standard deviation of the difference between the analyzed series and the linear (weighted) combination of explanatory series at each time point.

When the analyzed series is identical to one of the explanatory series, the optimizer does not converge -- instead of the usual result code 4 (gradient norm is no more than EpsG) it returns result code 7 (stopping conditions are too stringent; further improvement is impossible). However, I would expect the optimizer to simply assign a weight of 1 to the explanatory series identical to the analyzed series, and weights of 0 to all other series.

Is there a way to accomplish that via optimizer settings? (An obvious solution would be to check if any of the explanatory series equals the analyzed series before invoking the optimizer, but I'd rather avoid that.)

In general, the problem occurs if the analyzed time series is a linear combination of multiple explanatory time series. For example, if the analyzed time series is 60% of explanatory time series #1, 40% of explanatory time series #2, and 0% of N-2 other explanatory series from a set of N (where N > 2), then I would expect the MinBLEIC optimizer to produce weights of [0.6, 0.4, 0, 0, ..., 0] for the explanatory series. Instead, the optimizer stops with a termination type = 7.

Is there a way to configure the optimizer to come up with the right answer?