Quasi-Newton Updates with Bounds

We develop a quasi-Newton method which preserves known bounds on the Jacobian matrix. We show that this update can be computed with the same amount of work as competitive methods. In particular, we prove that the number of operations required to obtain this update is proportional to the number of no...

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Bibliographic Details
Published in:	SIAM journal on numerical analysis Vol. 24; no. 6; pp. 1434 - 1441
Main Authors:	Calamai, Paul H., More, Jorge J.
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01-12-1987
Subjects:	Algorithms Approximation Decomposition Exact sciences and technology Jacobians Linear transformations Mathematical vectors Mathematics Matrices Newtons method Nonlinear algebraic and transcendental equations Nonlinear equations Numerical analysis Numerical analysis. Scientific computation Perceptron convergence procedure Sciences and techniques of general use Sparsity Non linear equation Newton method Convergence Equation system
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Summary:	We develop a quasi-Newton method which preserves known bounds on the Jacobian matrix. We show that this update can be computed with the same amount of work as competitive methods. In particular, we prove that the number of operations required to obtain this update is proportional to the number of nonzeros in the sparsity pattern of the Jacobian matrix. The method is also shown to share the local convergence properties of Broyden's and Schubert's method.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/0724092