On the Local Convergence of Quasi-Newton Methods for Constrained Optimization

Boggs, Paul T.; Tolle, Jon W.; Wang, Pyng

doi:10.1137/0320014

Cited by 145 publications

(76 citation statements)

References 9 publications

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“…In this note we have presented what we consider to be a short, direct and self-contained derivation of the Boggs-Tolle-Wang characterization of g-superlinear convergence for quasi-Newton methods for constrained optimization. While we have stated that the three previous derivations (Boggs, Tolle and Wang [1]; Fontecilla, Steihaug and Tapia [4] and Nocedal and Overton [7]) leave something to be desired, we quickly add that the present work was strongly influenced by these three papers. Indeed, the basic idea that led to the present derivation was to attempt to parallel the Nocedal-Overton derivation using a formulation of the quasi-Newton method which possessed the attribute that all necessary differentiations could be obtained in a straightforward manner.…”

Section: Formulations Equivalent To Sqp the Materials In This Sectionmentioning

confidence: 79%

“…Boggs, Tolle and Wang [1] show that, under the assumption that the convergence of {x^.} to x* iŝ -linear, the convergence will also be g-superlinear,…”

mentioning

confidence: 99%

“…All three previous derivations of the Boggs-Tolle-Wang characterization leave something to be desired. The Boggs, Tolle and Wang [1] derivation is neither short nor direct and uses the unnecessary assumption of ^-linear convergence; however we emphasize that it was the first derivation. The Fontecilla, Steihaug and Tapia [4] derivation is lengthy and not direct.…”

mentioning

confidence: 99%

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On the characterization of 𝑞-superlinear convergence of quasi-Newton methods for constrained optimization

Stoer¹,

Tapia²

1987

Math. Comp.

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Section: Formulations Equivalent To Sqp the Materials In This Sectionmentioning

confidence: 79%

“…Boggs, Tolle and Wang [1] show that, under the assumption that the convergence of {x^.} to x* iŝ -linear, the convergence will also be g-superlinear,…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the characterization of 𝑞-superlinear convergence of quasi-Newton methods for constrained optimization

Stoer¹,

Tapia²

1987

Math. Comp.

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“…Work that has been directed to, or encompasses, the inequality-constrained problem includes that of [Han77], [ChaLLP82], [Sch83], and [GilMS86]. Han [BogTW82] can be carried over to the inequality-constrained problem in a straightforward inanner by using the projection onto the null space of the active constraint gradients.…”

mentioning

confidence: 99%

A merit function for inequality constrained nonlinear programming problems

Boggs¹,

Tolle²,

Kearsley³

1991

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“…Sufficient conditions for the Q-superlinear convergence of SQP methods under mild assumptions are that (see Boggs, Tolle and Wang [2]). That is to say, B (~) should map the null space correctly in the limit, but B (~) -W * is not necessary.…”

Section: When the Nlp Problem Has Nonlinear Constraints It Is Thementioning

confidence: 99%

A New Low Rank Quasi-Newton Update Scheme for Nonlinear Programming

Fletcher

IFIP International Federation for Information Processing

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A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transformations of the variables is preserved. The representation provides a limited memory capability, and there is an ordering scheme which enables 'old' information to be deleted when the memory is full. Hereditary and conjugacy properties are preserved to the maximum extent when minimizing a quadratic function subject to linear constraints. Practical experience is described on small (and some larger) CUTE test problems, and is reasonably encouraging, although there is some evidence of slow convergence on large problems with large null spaces.

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On the Local Convergence of Quasi-Newton Methods for Constrained Optimization

Cited by 145 publications

References 9 publications

On the characterization of 𝑞-superlinear convergence of quasi-Newton methods for constrained optimization

On the characterization of 𝑞-superlinear convergence of quasi-Newton methods for constrained optimization

A merit function for inequality constrained nonlinear programming problems

A New Low Rank Quasi-Newton Update Scheme for Nonlinear Programming

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