Upper Bounds on Combintorial Optimization Problems through an Augment...

Semidefinite programming proved to be a successful way to obtain high quality bounds to certain combinatorial optimization problems. Semidefinite problems can be solved by interior point methods. However, large-scale problems (i.e., Problems with a large number of variables and/or constraints) are intractable for solvers based on interior point methods. 

In this talk we will present an augmented Lagrangian approach to solve semidefinte programs. These methods apply an augmented Lagrangian approach to the dualsemidefinite problem where in each iteration a projection on to the cone of positive semidefinite matrices is performed. Furthermore, with the aim of improving the convergence rate of these methods, we propose to update the dual variables before the projection step. Numerical results demonstrate that this significantly decreases the over all numberof iterations within the augmented Lagrangian algorithm. 

Joint work with Marianna De Santis and Franz Rendl