> Your description of what "p" represents isn't very clear and you haven't described what q represents at all.
Sorry, I think my description was vague. Let me attempt to be more precise:
I have a set C which is the boundary of a (non-strict) convex set. You could imagine the boundary of a convex set, except instead of being curved, it has faces which are sections of hyperplanes (e.g. in 2D it would be a series of increasingly downward sloping lines).
Say "q" is a point on this set and "p" is a plane tangent to C at q (e.g. in 2D "p" is the slope of of a line tangent at q; at vertices there are multiple possible p).
I have a function f(q,p) and I want to solve for f(q,p) = zeros(n,1). What is the best method for doing so?