% file is s20.tex
BOUND 1 - Convex Quadratic Programming

Consider the shifted function
\[
 q_v(x) :=   x^t(Q - \diag(v))x + v^te +c^tx,
\]
and the relaxed problem
\[
  ~~(RP_v^1)~~~f_1(v) := \max_{-1 \leq x \leq 1} q_v(x).
\]
Then a bound for (P) is
\[
  B_1 := \min_{Q-\diag(v) \leq 0} f_1(v).
\]