I have an quadratic optimisation problem of the form
min w.r.t. to x 1/2 x'x + q'x S.t. Gx <= h
I have a rather big problem ( few million points and constraints), and while cvxopt's default solver proved effective, I'm curious about implementing it in SCS which should be faster (and without using the CVXPY interface).
After a literature search (mainly Boyd's Convex Analysis), the reformulation to SOCP-form should yield
min w.r.t. to z of c'z subject to Az + s = b, s in K
with c = (1 q)' and z = (t x)' where t is a scalar, and K is the cartesian product of the linear cones associated with my original constraints (Gx \leq h) and of a quadratic cone Q = { (t,x) | t >= ||x||}
However, how should I actually define A and b ?
I imagined something in the like of A = [[0 G],[2, 1, .., 1]] and b = (h 0). However, with the 'q' option set to [1] in the python scs.solve cone dictionary argument I can't get it to work ? What is the expected syntax of A's last line? (That is, assuming my mathematical reformulation is correct...)
Thank you for your help !
