IntervalNonlinearProblem kwargs not passed to solver

[lxvm]

Describe the bug 🐞

Although the IntervalNonlinearProblem docs say keyword arguments are passed to the solver, I do not find the solution to depend on the abstol passed to the problem (abstol does have an effect when passed to the solve). I only tested ITP.

Expected behavior

I would like to see that the abstol passed to the problem overrides the default abstol, but is of lower precedence than tolerances passed into solve.

Minimal Reproducible Example 👇

using SimpleNonlinearSolve
const counter = Ref(0)
prob = IntervalNonlinearProblem((x, counter) -> (counter[] += 1; exp(-x)-x), (0.0, 1.0), counter; abstol=1e-3)
solve(prob, ITP())
counter[] # 37
counter[] = 0
solve(prob, ITP(); abstol=1e-3)
counter[] # 9, fewer function evaluations than first, meaning the problem tolerance was not used

I was using SimpleNonlinearSolve.jl v2.1.0.

[ErikQQY]

Absolute tolerance needs to be specified in solve, in your first solve(prob, ITP()), ITP utilized the default abstol as real(oneunit(T)) * (eps(real(one(T))))^(4 // 5) which is approximately 3e-13. Then in your second solve(prob, ITP(); abstol=1e-3), the absolute tolerance is specified as 1e-3, hence fewer function evaluations.

[avik-pal]

Absolute tolerance needs to be specified in solve, in your first solve(prob, ITP()), ITP utilized the default abstol as real(oneunit(T)) * (eps(real(one(T))))^(4 // 5) which is approximately 3e-13. Then in your second solve(prob, ITP(); abstol=1e-3), the absolute tolerance is specified as 1e-3, hence fewer function evaluations.

The issue here is if we specify kwargs in IntervalNonlinearProblem, those should be forwarded to solve automatically.

Since we override https://github.com/SciML/NonlinearSolve.jl/blob/master/lib/BracketingNonlinearSolve/src/itp.jl#L59 directly, we should probably do kwargs = merge(prob.kwargs, kwargs) to resolve this