On second-order optimality conditions in nonlinear optimization. (2nd January 2017) - Andreani, Roberto; Behling, Roger; Haeser, Gabriel; Silva, Paulo J.S.
Abstract : In this work we present new weak conditions that ensure the validity of necessary second-order optimality conditions (SOC) for nonlinear optimization. We are able to prove that weak and strong SOCs hold for all Lagrange multipliers using Abadie-type assumptions. We also prove weak and strong SOCs for at least one Lagrange multiplier imposing the Mangasarian–Fromovitz constraint qualification and a weak constant rank assumption.