Improving robustness of the solvers

[MaxenceGollier]

I stumbled accross this chapter from Conn Gould and Toint where a lot of algorithmic details is given.

• They discuss the issues of catastrophic cancellations when computing $$m(x+s) - m(x)$$ as well as $$f(x+s) - f(x)$$.
• There are suggestions for choosing an appropriate initial value of $$\Delta_0$$ (which could be easily generalized to $$\sigma_0$$ and the nonsmooth context).
• They discuss the situation where $$\rho_k < 0$$.

I have other things in mind, namely we should

• Try to implement as much as possible statuses from SolverCore.jl and decide what to do in each case (for example, if the subsolver returned unbounded we could try increasing $$\sigma$$.)
• Decide what to do with the $$\xi < 0$$ situation

There are definitely other things, I opened it as a discussion because it is too vague to be a dedicated issue.