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
ScaLAPACK user's guide
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming
Computational Optimization and Applications
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Lagrangian Dual Interior-Point Methods for Semidefinite Programs
SIAM Journal on Optimization
SIAM Journal on Optimization
Solving Some Large Scale Semidefinite Programs via the Conjugate Residual Method
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
High Performance Grid and Cluster Computing for Some Optimization Problems
SAINT-W '04 Proceedings of the 2004 Symposium on Applications and the Internet-Workshops (SAINT 2004 Workshops)
Implementation of a primal—dual method for SDP on a shared memory parallel architecture
Computational Optimization and Applications
Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A parallel interior point decomposition algorithm for block angular semidefinite programs
Computational Optimization and Applications
Exploiting equalities in polynomial programming
Operations Research Letters
Abstract interpretation meets convex optimization
Journal of Symbolic Computation
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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The SDPA (SemidDefinite Programming Algorithm) is known as efficient computer software based on the primal-dual interior-point method for solving SDPs (SemiDefinite Programs). In many applications, however, some SDPs become larger and larger, too large for the SDPA to solve on a single processor. In execution of the SDPA applied to large scale SDPs, the computation of the so-called Schur complement matrix and its Cholesky factorization consume most of the computational time. The SDPARA (SemiDefinite Programming Algorithm paRAllel version) is a parallel version of the SDPA on multiple processors and distributed memory, which replaces these two parts by their parallel implementation using MPI and ScaLAPACK. Through numerical results, we show that the SDPARA on a PC cluster consisting of 64 processors attains high scalability for large scale SDPs without losing the stability of the SDPA.