Identifying no-roots case

[ivborissov]

Hi,
I am solving optimization problem (ODE parameters estimation) and as a result I have 4 values param_1 , param_2 , param_3, param_4 marking minimum of loss_func. Now I need to find intersections of loss_func(param_i) with some critical level alpha = const. Typically loss_func(param_i) has parabolic shape with 2 intersections or "semi-constant shape with little bifurcations" and no intersections with alpha. For parabolic case Roots.jl derivative-free algorithms (order 0, 2, 8) work perfect but for "semi-constant" case it either fails to approximate derivatives or reaches maxevals. I am looking for roots search algorithm that can identify that "semi-constant" case and efficiently explore all the search area (1e-9,1e9) to say that there are no roots. Do you have an idea how it can be achieved?

[jverzani]

Boy, that seems like a tough thing to do in general. The fzeros function does a naive approach of splitting the interval into many sub intervals and then searches for bracketing cases. This will not guarantee all zeros are found. I'm not sure exactly how regular your "semi-constant" cases are. You might try tracing the algorithm through verbose=TRUE to see what happens.

[ivborissov]

I see, thanks