(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Theorem:

Let f: M->R

where M is a open subset of R^{n}

Suppose f is C^{2}(M)

Let x E M such that

"gradient of f at x" = 0 and the Hessian of f at x is positive definite

Then x is astrict local minimum pointof f.

The above theorem is given in my textbook.

If instead we have "gradient of f at x" = 0 and the Hessian of f at x is positive SEMI-definite, can we conclue that x is alocal minimumpoint of f? Why or why not?

This puzzles me and I can't find this in the textbook.

2. Relevant equations

Unconstrained optimziation

3. The attempt at a solution

N/A

Any help is appreciated!

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# Unconstrained optimziation: Local minimum

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