Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality
Alexander Davidovich Ioffe · SIAM Journal on Control and Optimization · 1979
The paper contains second order necessary and sufficient conditions for a minimum, exact smooth penalty theorems and augmented Lagrangian duality theorems which cover the case when more than one collection of Lagrange multipliers exist and the second order quadratic function can be lower estimated only by norms weaker than that in which the cost function and constrained mappings are differentiable.