don't propagate non-finite residuals

[tpapp]

Problem

When the residuals are not finite (eg Inf or NaN), the solver propagates them into the next call, which usually leads to things silently iterating until the maximum number of iterations are exhausted, without a warning.

An MWE is

using NLsolve

function f(x)
    any(isnan, x) && printstyled("things went south\n"; color = :red)
    @show x
    map(x -> 0.2 < abs(x) < 1 ? oftype(x, NaN) : x^3, x)
end

nlsolve(f, fill(1.1, 3), autodiff = :forward, iterations = 50, method = :newton)

Not sure if #228 is related.

Suggestions

1. At least a sanity check terminating the solver and returning as non-converged would avoid doing meaningless iterations. This would be a quick fix.

2. A heuristic algorithm could potentially recover from this by shrinking the steps taken until everything is finite, but that's more complex.

[pkofod]

If the static line search is used, this should definitely be caught somewhere, and the solver should stop. If a line search is used, it will keep halving the steps until a finite value is encountered. Thanks