I have the following non convex problem
\begin{array}{ll} &\min_{x}f(x)& \\ &\text{s.t. }g(x)=0& \end{array}
Where I have a particular $f$ and $g$. To solve this problem in my case I found that it was much easier to solve the sequence of the following regularized problems.
$$\text{arg}\min_{x} f(x) + \lambda|g(x)|$$
Where I make $\lambda$ grow and initialize $x$ with the last solution found. I make $\lambda$ bigger when $x$ stagnates. I am sure this method already exists but I can't find its name. I know in convex optimization there is the interior point method that resembles this but they do this in the case of inequality constraints. Also I think it no longer qualifies as an interior point method if it is not applied to a convex problem? I am guessing this would fit in penalized optimisation methods but I can't find references similar to my problem.
