Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
ACM Transactions on Mathematical Software (TOMS)
Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
SIAM Journal on Optimization
| Hi-index | 0.00 |
Semidefinite programming (SDP) covers a wide range of applications such as robust optimization, polynomial optimization, combinatorial optimization, system and control theory, financial engineering, machine learning, quantum information and quantum chemistry. In those applications, SDP problems can be large scale easily. Such large scale SDP problems often satisfy a certain sparsity characterized by a chordal graph structure. This sparsity is classified in two types. The one is the domain space sparsity (d-space sparsity) for positive semidefinite symmetric matrix variables involved in SDP problems, and the other the range space sparsity (r-space sparsity) for matrix-inequality constraints in SDP problems. In this short note, we survey how we exploit these two types of sparsities to solve large scale linear and nonlinear SDP problems. We refer to the paper [7] for more details.