Augmented Lagrangian approaches for Large Scale Semidefinite Programming
| Componente | Categoria |
|---|---|
| Federico Battista | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca |
| Francisco Facchinei | Componenti strutturati del gruppo di ricerca |
| Antonio Sassano | Componenti strutturati del gruppo di ricerca |
| Marco Boresta | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca |
Semidefinite Programming refers to optimization problems where the vector variable is a symmetric matrix constrained to be positive semidefinite.
Interest on semidefinite programming has grown tremendously during the last two decades and this is partly due to the fact that many practical problems in operations research and combinatorial optimization can be modeled or approximated by semidefinite programs.
Furthermore, semidefinite programs can be solved in polynomial time by interior point methods. However, when the dimension of the problem and the number of constraints get large, interior point methods become impractical both in terms of computation time and memory requirements.
It is the purpose of the present project to focus on augmented Lagrangian methods, known to be an alternative to interior point methods for solving large-scale semidefinite programs.
In our project, we plan to devise, implement and test new augmented Lagrangian algorithms for solving large-scale semidefinite programs. We also plan to focus on structured semidefinite programs, obtained as continuous relaxation of specific combinatorial optimization problems.
The augmented Lagrangian methods developed will represent an efficient tool to compute valid bounds on the optimal solution of the combinatorial problems considered.