Best discussion of the bordered Hessian ever!

Ever wanted to know why the positive semi-definiteness condition on the bordered Hessian characterizes the maximum in a constrained optimization problem?

Yeah, me too.

I guess I never made the connection that when I put the constraints, multiplied by the Lagrangians, in the objective function, I was treating the constrained problem as an unconstrained problem. Unconstrained problems have their second order conditions characterized by a positive semi-definite Hessian. The bordered Hessian is just the Hessian of the new problem. Va bene!

Not sure why I never made that connection before…