A Second Order Method for the Linearly Constrained Nonlinear Programming Problem

An algorithm using second derivatives for solving the problem: minimize f(x) subject to Ax − b ≥ 0 is presented. Convergence to a Second-Order Kuhn Tucker Point is proved. If the strict second-order sufficiency conditions hold, the rate of convergence of the algorithm is shown to be superlinear or e...

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Veröffentlicht in:Nonlinear Programming S. 207 - 243
1. Verfasser: McCORMICK, GARTH P.
Format: Buchkapitel
Sprache:Englisch
Veröffentlicht: United States Elsevier Inc 1970
Elsevier Science & Technology
Schlagworte:
Applied mathematics
ISBN:9780125970501, 148327246X, 9781483245638, 9781483272467, 1483245632, 0125970501
Online-Zugang:Volltext
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Zusammenfassung:An algorithm using second derivatives for solving the problem: minimize f(x) subject to Ax − b ≥ 0 is presented. Convergence to a Second-Order Kuhn Tucker Point is proved. If the strict second-order sufficiency conditions hold, the rate of convergence of the algorithm is shown to be superlinear or even quadratic with aLipschitz condition on the second derivatives of f(x).
ISBN:9780125970501
148327246X
9781483245638
9781483272467
1483245632
0125970501
DOI:10.1016/B978-0-12-597050-1.50011-7