Suppose f(): R" → R, G(.) : R” → R", and H(.) : R" → RP are functions. Consider the optimization problem (P) min f(x) over G(x) ≤0, H(x) = 0. #3) Suppose now p = 0 (no equality constraints), € argmin(P) and the Constraint Qualification holds. What is the first order necessary condition for the optimality of x?

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Suppose f(): R" → R, G(.) : R" → R", and H(.) : R" → Rº are functions. Consider the optimization
problem
(P)
min f(x) over G(x) ≤0, H(x) = 0.
#3) Suppose now p = 0 (no equality constraints), X = argmin(P) and the Constraint Qualification holds. What is
the first order necessary condition for the optimality of x?
Transcribed Image Text:Suppose f(): R" → R, G(.) : R" → R", and H(.) : R" → Rº are functions. Consider the optimization problem (P) min f(x) over G(x) ≤0, H(x) = 0. #3) Suppose now p = 0 (no equality constraints), X = argmin(P) and the Constraint Qualification holds. What is the first order necessary condition for the optimality of x?
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