In this talk, we give a theoretical and numerical insight into a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints are nonconvex and complicated, like cardinality constraints, disjunctive programs, or matrix problems involving rank constraints. The method presented here explicitly handles these difficult constraints, thus generating iterates which are feasible with respect to them, while the remaining (standard and supposingly simple) constraints are tackled by sequential penalization. Therefore, we are dealing with a significant generalization of existing penalty decomposition methods. On the other hand, the topic is related to some recent publications which use an augmented Lagrangian idea to solve optimization problems with geometric constraints. Compared to these methods, the decomposition idea appears to have some appealing computational features. Extensive numerical results on several highly complicated classes of optimization problems in vector and matrix spaces indicate that the current method is indeed very efficient to solve these problems.
Link to the paper: https://arxiv.org/abs/2210.05379
Personal Website of Matteo Lapucci
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: November 28, 2022, 4.30 pm Vienna
Meeting ID: 651 4141 3205
Password: 086933