On second-order optimality conditions in nonlinear optimization
Roberto Andreani, Roger Behling, Gabriel Haeser, Paulo J. S. Silva · Optimization methods & software · 2016
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.