+1 for the "whence" in that final sentence...

I'm confused: aren't you trying to minimize the distance to a fixed $x \in \mathbb{R}^n$ constrained by a single convex inequality? It sounds like "distance to $x$" is the function that you should use. Have I misunderstood?

Have you tried minConf? di.ens.fr/~mschmidt/Software/minConf.html

Good idea, I've just sent him an email. I will post an answer here if and when he responds.

Donu, I agree that it seems strong. But the question is natural: in the filtered derived category, does the equivalence $C \sim C'$ iff $E(C)$ is isomorphic to $E(C')$ go by another name?

Thank you for the answer, I've just taken a look at Brown. As you have said, the result already presupposes the existence of a filtered chain map. Do you know if it is possible to induce such an $f$ from the given isomorphism of spectral sequences? In any case, if no one makes a stronger statement than yours soon then I will accept this answer.