Suppose that the constraint correspondence G(y) in the constrained optimization problem (example 2.30) is defined by a
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is defined by a set of inequalities (example 2.40)
g1(x, θ) ¤ 0, g2(x, θ) ¤ 0, ... , gm (x, θ) ¤ 0
If each functional gj (x; θ) F(X à Î) is convex jointly in x and y, then the correspondence
G(θ) = {x X: gj(x, θ) ¤ 0, j = 1,2, ... , m}
is convex.
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