Add caching for solvers without init

[avik-pal]

This is needed because we want to write generic code with init and solve! without having to query every solver to check if it supports caching.

[codecov]

Codecov Report

Attention: 6 lines in your changes are missing coverage. Please review.

Comparison is base (bf072d2) 88.11% compared to head (e37b70a) 87.95%.

Files	Patch %	Lines
ext/NonlinearSolveLeastSquaresOptimExt.jl	0.00%	2 Missing ⚠️
src/abstract_types.jl	0.00%	2 Missing ⚠️
src/core/noinit.jl	81.81%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #382      +/-   ##
==========================================
- Coverage   88.11%   87.95%   -0.16%     
==========================================
  Files          45       46       +1     
  Lines        2675     2690      +15     
==========================================
+ Hits         2357     2366       +9     
- Misses        318      324       +6     

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[avik-pal]

I will do a little bit of type piracy for SimpleNonlinearSolve to avoid having to copy over this code there.

Also because caching interface comes into play when NonlinearSolve compatibility is needed

[ChrisRackauckas]

does this effect type inference? I don't see why this wouldn't be concrete as well.

[avik-pal]

this is needed because cache.kwargs = merge(cache.kwargs, kwargs) can change the type in reinit

[ChrisRackauckas]

I will do a little bit of type piracy for SimpleNonlinearSolve to avoid having to copy over this code there.

That seems reasonable.