Relax primal-dual system upon linesearch failure

[dfridovi]

Adjusts \epsilon as follows:

• if linesearch succeeds: \epsilon *= 1 - exp(-iters)
• if linesearch fails: \epsilon *= 1 + exp(-iters)

This fixes #7.

[lassepe]

I thought I had tested something like this and concluded that it wasn't enough because it cycles. Maybe try my MVP from #7 as a test?

[dfridovi]

I think the runtests.jl file should have exactly that MVP, no?

[lassepe]

M is different: M = [0 1; -1 0]

[dfridovi]

Right... helps to read ;) So that M makes the QP not convex if I am not mistaken, and therefore I think with these constraints it is going to be an ill-posed problem for some choices of \theta. That explains why it was having trouble. I've added a "fix" that just errors out after a fixed number of outer loop iterations now.

[dfridovi]

Ah I see - basically the quadratic term will evaluate to zero for all x. Then the well posedness entirely depends on the sign of theta.

[lassepe]

This is never used. Intended?

[dfridovi]

Good catch