Suppose two optimality cuts (1.4) are active for (x t k,θ t k ) for any t and k . Show that either the sub problems generate a new cut with θ t k > θ t k or an optimal solution of NLDS(t +1, j) with...

Suppose two optimality cuts (1.4) are active for (x_t
k,θ t_k) for any t and k . Show that either the sub problems generate a new cut with θ_t
k > θ_t
k or an optimal solution of NLDS(t +1, j) with input xt k for some scenario
 must be degenerate.