weighted convex opt svi -- just multiplying through by weights... (thx kevin)

optimize_weighted.py

def optimize_weighted(y,max_vi,weights,market_vols,tte,s):
# {{{
    y    = y[market_vols>0]
    vols = market_vols[market_vols>0]
    w    = weights[market_vols>0]
    n = len(y)

    # R ends up n by 3
    R = np.concatenate([np.ones(n), np.sqrt(y**2+1), y]).reshape(3,n).T

    # W is n by n 
    W = np.diag(w)

    Q = 2*matrix(R.T.dot(W).dot(R))


    #Y1  = np.sum(y)
    #Y2  = np.sum(y**2)
    #Y3  = np.sum(np.sqrt(y**2+1))
    #Y4  = np.sum(y*np.sqrt(y**2+1))
    #Y5  = np.sum(y**2+1)

    var_t = vols**2*tte

    #v   = np.sum(var_t)
    #vsq = np.sum(var_t*var_t)
    #vY  = np.sum(var_t*y)
    #vY2 = np.sum(var_t*np.sqrt(y**2+1))

    q = -2*matrix(var_t.T.dot(W).dot(R))

    h = matrix([0.0, 4.0*s, 0.0, 0.0, 4.0*s, 4.0*s, 0.0, max_vi])

 
    # G is in column-major order
    G = matrix([[0.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0],[-1.0,1.0,-1.0,-1.0,1.0,1.0,0.0,0.0],[0.0,0.0,-1.0,1.0,-1.0,1.0,0.0,0.0]])

    cvxopt.solvers.options['show_progress'] = False
    sol = solvers.qp(Q,q,G,h)
 
    # I convert back to the notation in the paper here
    # to verify that the constraints are satisfied:
    a = sol['x'][0]
    c = sol['x'][1]
    d = sol['x'][2]
 
    if(c < 0 or c > 4*s):
        print "Failed first constraint\n"
    if(math.fabs(d) > c or math.fabs(d) > ((4*s) -c)):
        print "Failed second constraint\n"
    # This constraint differs in the paper from the one Josh originally sent; 
    # I use the one from the paper
    if(a < 0.0 or a > max_vi):
        print "Failed third constraint\n"
 
    return sol['x']