Prove corollary 5.2.3.
We will not prove the second part of corollary 5.2.2, since it will not be used elsewhere in the book (see Luenberger 1984, p. 226; Simon 1986, p. 85). Instead we develop below (corollary 5.2.4, section 5.4.3) some global conditions that are useful in practice.
Suppose there exists x* ˆˆ X and λ ˆˆ Rm such that

2. HL(x*) is negative definite on the hyperplane tangent to g, that is, xTHL(x*) (x) Then x* is a strict local maximum of maxxˆˆX f(x) subject to g(x) = 0.

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