Add 3 equality-constrained, regularized problems

[MaxenceGollier]

I am interested in solving

$$\min_x f(x) + h(x) \quad \text{s.t} \ c(x) = 0,$$

where every function can be non-convex and $$f$$ and $$c$$ are smooth.
I wish to implement

• The convex and non-convex Basis-Pursuit problems: $$min_x \lVert x \rVert_1$$ and $$min_x \lVert x \rVert_0$$ subject to $$Ax = b$$ : Add basis pursuit model #89.
• The Low rank matrix completion problem
• The FH problem; this problem can be reformulated as $$\min_x \int |u(x,t) - u_{obs}(t)|^2 dt + \lVert x \rVert_0 $$ subject to $$du/dt = F(t,u,x)$$, we can use PDENLPModels.jl to model the smooth part of this problem.