My fault for not having looked at the ALGLIB contents closer in a rush to implement things quickly. I found the MinASA module which accepts constraints as ranges for each X in a vector. Since in my optimization the sum of all Xs has to be 1 and all Xs have to be nonnegative, I simply specified the lower bound of 0 and upper bound of 1 for each X. The results are fine in that respect. But how to properly implement the constraint of the sum of all Xs to be 1? I tried the following:  At each iteration, I sum up all Xs in a variable "xsum"  Add a term "Square(xsum  1.0)" to st.F  Add a term "2.0 * (xsum  1.0)" to each st.G(i)
That seems to work but only roughly. The resulting sum of Xs is typically in the .997 to 1.03 range, which is too big an error for my liking. I tried various combinations of EpsG, EpsX, and EpsX to no effect. I tried to calculate the gradient for each X using 4 points instead of just 2 points (as Sergey suggested be done for MinLBFGS). A slight improvement resulted but it still does not work perfectly (a reference implementation with Solver in Excel does, in that all Xs always sum up to 1 as prescribed).
Could anyone offer any pointers on how to solve that? Esp. how to properly calculate a gradient of a nonlinear function with accuracy. Thanks in advance.
