Show that 2 is a relaxation of 1

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An optimization problem(1)can be viewed as defining a function: S → R, where S is the feasible set of (1).

The epigraph of f is the set {(z, x) | z ≥ f(x), x ∈ S}.

Show that (2) is a relaxation of (1) if and only if the projection of the epigraph of f' onto (z, x) contains the epigraph of f. ¹

Reference no: EM131168561

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