Second order optimization methods (Q1309072)

The paper begins with a new form of the second-order necessary conditions for a local optimal solution to a constrained minimization problem involving equality constraints. Then, it is proved that each limiting point of a sequence generated by quadratic penalty methods is a 2- stationary point (i.e., a point at which the previous necessary conditions are satisfies). The problem of constructing numerical methods of unconstrained optimization guaranteeing convergence to 2-stationary points is investigated. Finally, an extension to minimization problems with constraints given as inequalities is considered. An algorithm using a technique applied in methods of feasible directions is provided.