# Surrogate relaxation

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Solving the surrogate dual problem, see the supplement on duals. For given multipliers $LaTeX: \textstyle (u,v) (u \ge 0),$ the surrogate dual objective is the relaxed mathematical program:

$LaTeX: \max \left \{f(x) : x \in X, ug(x) \le 0, vh(x) = 0 \right \}.$

(More generally, the surrogate could be a nonlinear combination of the constraints.)