Augmented Lagrangian Applied to Convex Quadratic Problem Solution

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadratic problem is formed by, in the current point, a quadratic approach of the Lagrangian function associated with the original problem and the linearization of approach of the constraints. After that we use penalization to solve these subproblems using the Augmented Lagrangian algorithms with quadratic penalty, what results in a sequence of unconstrained quadratic problems, that compared with the original problem can be considered of easier solution. Through this new methodology we show that if the Lagrangian function associated with the original problem is strict convex (convex), then the hessian matrix of Augmented Lagrangian function is defined positive (semidefined positive), then satisfies the sufficient condition optimality of second order. AMS subject classification: 65F10