Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Parallel programming with MPI
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
SDPARA: semiDefinite programming algorithm paRAllel version
Parallel Computing
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics)
SIAM Journal on Optimization
Solving large-scale semidefinite programs in parallel
Mathematical Programming: Series A and B
Decomposition-Based Interior Point Methods for Two-Stage Stochastic Semidefinite Programming
SIAM Journal on Optimization
Implementation of a primal—dual method for SDP on a shared memory parallel architecture
Computational Optimization and Applications
Nonlinear Optimization
SIAM Journal on Optimization
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We present a two phase interior point decomposition framework for solving semidefinite (SDP) relaxations of sparse maxcut, stable set, and box constrained quadratic programs. In phase 1, we suitably modify the matrix completion scheme of Fukuda et al. (SIAM J. Optim. 11:647---674, 2000) to preprocess an existing SDP into an equivalent SDP in the block-angular form. In phase 2, we solve the resulting block-angular SDP using a regularized interior point decomposition algorithm, in an iterative fashion between a master problem (a quadratic program); and decomposed and distributed subproblems (smaller SDPs) in a parallel and distributed high performance computing environment. We compare our MPI (Message Passing Interface) implementation of the decomposition algorithm on the distributed Henry2 cluster with the OpenMP version of CSDP (Borchers and Young in Comput. Optim. Appl. 37:355---369, 2007) on the IBM Power5 shared memory system at NC State University. Our computational results indicate that the decomposition algorithm (a) solves large SDPs to 2---3 digits of accuracy where CSDP runs out of memory; (b) returns competitive solution times with the OpenMP version of CSDP, and (c) attains a good parallel scalability. Comparing our results with Fujisawa et al. (Optim. Methods Softw. 21:17---39, 2006), we also show that a suitable modification of the matrix completion scheme can be used in the solution of larger SDPs than was previously possible.