% file is s18.tex
{\bf Three Relaxations}\\
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relaxed problem
\[
  ~~(RP_v^1)~~~f_1(v) := \max_{-1 \leq x \leq 1} q_v(x).
\]
bound
\[
  B_1 := \min_{Q-\diag(v) \leq 0} f_1(v).
\]
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relaxed problem
\[
  ~~(RP^2_u)~~~f_2(u) := \max_{||y||^2=n} q_u(y).
\]
bound
\[
  B_2 := \min_{u^te=0} f_2(u) = \min_{u} f_2(u).
\]