Characterizing the second-order sufficient optimality condition by a primal-dual quadratic growth condition

DAMIÁN FERNÁNDEZ

Guanajuato

Congreso; Mathematical Congress of the Americas (MCA) 2013; 2013

CIMAT, Centro de Investigación en Matemáticas

The second-order sufficient optimality condition (SOSC) is a commom hypothesis in the local convergence analysis of many computational methods for nonlinear optimization problems. This is the case for the augmented Lagrangian (AL) method. Second-order derivatives are needed in the convergence analysis even where second derivatives are not needed in the method. We show that subproblems of the AL are solvable under some primal-dual quadratic growth condition. Moreover, for twice differentiable functions this quadratic growth condition is equivalent to SOSC.