(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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Unconstrained optimziation: Local minimum

**Physics Forums | Science Articles, Homework Help, Discussion**