Deal with zero dual residual

[lukevolpatti]

Some problems start with zero dual residual and keep zero dual residual until the first rho update. This makes QSS want to set rho to infinity. To mitigate this, QSS never sets rho higher than RHO_MAX, currently 1e6. However, in some cases even this is too high, and numerous refactorizations need to be done to bring rho back down to something reasonable.

Example that has this kind of issue:

np.random.seed(1234)
p = 1000  # 300
n = 2000  # 800
constr_dim = 200
G = sp.sparse.random(n, p, density=0.01, format="csc")
h = 10 * (np.random.rand(n) - 0.5)

lmda = 150

data = {}
data["P"] = G.T @ G
data["q"] = -h.T @ G
data["r"] = 0.5 * h.T @ h
data["A"] = sp.sparse.random(constr_dim, p, density=0.1, format="csc")
data["b"] = np.random.rand(constr_dim)
data["g"] = [{"g": "abs", "args": {"weight": lmda}, "range": (0, p)}]

data["P"] = sp.sparse.csc_matrix(data["P"])

This can perhaps be partially fixed by making it so rho can never increase nor decrease by a factor of more than, say, 100 at a time.