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An interior point method for quadratic programs based on conjugate projected gradients. (English) Zbl 0778.90048
Summary: We propose an interior point method for large-scale convex quadratic programming where no assumptions are made about the sparsity structure of the quadratic coefficient matrix \(Q\). The interior point method we describe is a doubly iterative algorithm tha invokes a conjugate projected gradient procedure to obtain the search direction. The effects is that \(Q\) appears in a conjugate direction routine rather than in a matrix factorization. By doing this, the matrices to be factored have the same nonzero structure as those in linear programming. Further, one variant of this method is theoretically convergent with only one matrix factorization throughout the procedure.

MSC:
90C20 Quadratic programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C25 Convex programming
Software:
ALPO; GAMS; MINOS
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