On the Solution of Equality Constrained Quadratic Programming Problems arising in Optimization

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Persistent URL	http://purl.org/net/epubs/work/29752
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Record Id	29752
Title	On the Solution of Equality Constrained Quadratic Programming Problems arising in Optimization
Contributors	N I M Gould, M E Hribar, J Nocedal
Abstract	We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in non-linear optimization. Our approach is based 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. This can yield substantial economies in both line search and trust region methods for large-scale optimization, but can also result in significant rounding errors. We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring in high computational overhead. Numerical results illustrating the efficiency of the proposed approaches are presented.
Organisation	CCLRC
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-1998-069. 1998.		raltr-1998069.pdf	1998