Is it necessary that the Hessian matrix of the objective function always be positive definite in an unconstrained minimization problem? Cite two circumstances in which the use of the simplex method of...

Is it necessary that the Hessian matrix of the objective function always be positive definite in an unconstrained minimization problem? Cite two circumstances in which the use of the simplex method of multivariate unconstrained optimization might be a better choice than a quasi-Newton method.