Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
SDPARA: semiDefinite programming algorithm paRAllel version
Parallel Computing
Solving Large Scale Semidefinite Programs via an Iterative Solver on the Augmented Systems
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
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Large-scale semidefinite programs in electronic structure calculation
Mathematical Programming: Series A and B
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
Implementation of a primal—dual method for SDP on a shared memory parallel architecture
Computational Optimization and Applications
Algorithm 875: DSDP5—software for semidefinite programming
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
Mathematical Programming: Series A and B - Special Issue on Cone Programming and its Applications
ACM Transactions on Mathematical Software (TOMS)
High-performance general solver for extremely large-scale semidefinite programming problems
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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A SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical optimization. SDP provides an effective computation framework for many research fields. Some applications, however, require solving a large-scale SDP whose size exceeds the capacity of a single processor both in terms of computation time and available memory. SDPARA (SemiDefinite Programming Algorithm paRAllel package) [Yamashita et al. 2003b] was designed to solve such large-scale SDPs. Its parallel performance is outstanding for general SDPs in most cases. However, the parallel implementation is less successful for some sparse SDPs obtained from applications such as Polynomial Optimization Problems (POPs) or Sensor Network Localization (SNL) problems, since this version of SDPARA cannot directly handle sparse Schur Complement Matrices (SCMs). In this article we improve SDPARA by focusing on the sparsity of the SCM and we propose a new parallel implementation using the formula-cost-based distribution along with a replacement of the dense Cholesky factorization. We verify numerically that these features are key to solving SDPs with sparse SCMs more quickly on parallel computing systems. The performance is further enhanced by multithreading and the new SDPARA attains considerable scalability in general. It also finds solutions for extremely large-scale SDPs arising from POPs which cannot be obtained by other solvers.