Suppose that (x*, y*) is a local optimum of subject to g(x, y) = 0 and y

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Suppose that (x*, y*) is a local optimum of
Suppose that (x*, y*) is a local optimum ofsubject to

subject to g(x, y) = 0 and y > 0
and a regular point of g. Then there exist multipliers λ1, λ2, . . . , λm such that

Suppose that (x*, y*) is a local optimum ofsubject to

With

Suppose that (x*, y*) is a local optimum ofsubject to
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