Using DiffEqBase.NLSolveTerminationCondition in NonlinearSolve.jl

Specific Domains Optimization (Mathematical)
, ,
1

I am trying to solve a system of three nonlinear equations and would like to use the termination conditions provided by DiffEqBase.NLSolveTerminationCondition (see the documentation of NonlinearSolve.jl.

The function definitions in my problem are of the form

f!(r,param,a) = eq_bin!(r, param, kappa, gamma, a; verbose = verbose::Bool)

J!(J,param,a) = eq_bin_jac!(J, param, kappa, gamma, a, v) 
   

function Jv!(Jv,vec,param,a) 
        eq_bin_jac!(J, param, kappa, gamma, a, v) 
        mul!(Jv,J,vec) 
        return nothing 
end 

function Jvt!(Jv,vec,param,a) 
    eq_bin_jac!(J, param, kappa, gamma, a, v) 
    mul!(Jv,J',vec)  
    return nothing 
end

NF = NonlinearFunction{true, specialize}(f!; 
    jac = J!, 
    jvp = Jv!, 
    vjp = Jvt!, 
    jac_prototype = jp
)

which I want to solve using

probN = NonlinearProblem(NF, x_init, a)
sol = solve(probN, method, reltol = reltol, abstol = abstol, maxiters = maxiters)

Now it sometimes happens with unfortunate starting values, that my system blows up, or that I do not get an improvement over a series of iterations of my system. Hence, I would like to use
NLSolveTerminationCondition(NLSolveTerminationMode.AbsSafeBest).

However, I do not understand where I should put this termination condtion in my solver setup. solve does not have an obvious suitable kwarg and nor does NonlinearProblem from what I saw.

Any help as to how to use the termination condition funcitonality is greatly appreciated.

2

What method are you using?

4

TrustRegion() and NewtonRaphson() from NonlinearSolve. The fromer has a tendency to get stuck, while the latterr often blows up.

5

They aren’t using the new termination conditions quite yet. @Oscar_Smith probably a good time to finish add TerminationCondition support to NewtonRaphson by oscardssmith · Pull Request #162 · SciML/NonlinearSolve.jl · GitHub ?

6

That is unfortunate, so my best shot is to mimick the behaviour using callbacks I suppose?

I was just trying to use isoutofdomain to reject steps wehre the solution blows up or is negative using
isoutofdomain = (u,p,t)->any(x -> (x < 0 || abs(x) > 1e4), u) but I still get the same negative values and solutions that blow up as if I was using no isoutofdomain. Also tried the callback = PositiveDomain() which did not do anything for me either. Solver was again NewtonRaphson(). Any ideas on how to make this work?