## On the solution of equality constrained quadratic programming problems arising in optimization (1998)

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Venue: | SIAM J. Sci. Comput |

Citations: | 41 - 2 self |

### BibTeX

@ARTICLE{Gould98onthe,

author = {Nicholas I. M. Gould and Mary E. Hribar},

title = {On the solution of equality constrained quadratic programming problems arising in optimization},

journal = {SIAM J. Sci. Comput},

year = {1998},

volume = {23},

pages = {1376--1395}

}

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### Abstract

Jorge Nocedal z We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based implicitly on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computing projections into the null space by either a normal equations or an augmented system approach. Unfortunately, in practice such projections can result in signi cant rounding errors. We propose iterative re nement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads. Numerical results illustrating the e cacy of the proposed approaches are presented. Key words: conjugate gradient method, quadratic programming, preconditioning, largescale optimization, iterative re nement.