Optimality Conditions: Unconstrained

This lecture covers Fermat's theorem stating that x* is a local minimum of f if f is differentiable around x* and Vf(x*) = 0. It also discusses necessary optimality conditions, such as the positive semidefinite condition for twice differentiable functions and examples illustrating the concept. Additionally, the lecture explores second derivatives, convexity, and eigenvalue curvature in the context of optimization.