A centered projective algorithm for linear programming
Mathematics of Operations Research
An OnL iteration potential reduction algorithm for linear complementary problems
Mathematical Programming: Series A and B
An OL(n3) potential reduction algorithm for linear programming
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
ScaLAPACK user's guide
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
Nonlinear optimization and parallel computing
Parallel Computing - Special issue: Parallel computing in numerical optimization
Inner solvers for interior point methods for large scale nonlinear programming
Computational Optimization and Applications
Some iterative methods for the solution of a symmetric indefinite KKT system
Computational Optimization and Applications
Computational Optimization and Applications
A parallel dual-type algorithm for a class of quadratic programming problems and applications
Expert Systems with Applications: An International Journal
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This paper deals with a parallel implementation of an interior point algorithm for solving sparse convex quadratic programs with bound constraints. The parallelism is introduced at the linear algebra level. Concerning the solution of the linear system arising at each step of the considered algorithm, we use an iterative approach based on the conjugate gradient method and on a block diagonal preconditioning technique. Moreover, we apply an incomplete Cholesky factorization with limited memory into each block, in order to put together the high degree of parallelism of diagonal preconditioning techniques and the greater effectiveness of incomplete factorizations procedures. The goal is to obtain an efficient parallel interior point solver for general sparse problems. Results of computational experiments carried out on an IBM SP parallel system by using randomly generated very sparse problems without a particular structure are presented. Such results show that the considered inner iterative approach allows to obtain a constant CPU time reduction as the number of processors used increases.