Perturbation Lemma for the Newton Method with Application to the SQP Newton Method

D. Cores and R. A. Tapia
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D. Cores: INTEVEP, Research Center of the Venezuelan Oil Company
R. A. Tapia: Rice University

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 2, No 2, 280 pages

Abstract: Abstract We study the convergence of a general perturbation of the Newton method for solving a nonlinear system of equations. As an application, we show that the augmented Lagrangian successive quadratic programming is locally and q-quadratically convergent in the variable x to the solution of an equality constrained optimization problem, under a mild condition on the penalty parameter and the choice of the Lagrange multipliers.

Keywords: Newton's method; augmented Lagrangian; successive quadratic programming; quadratic convergence; Lagrange multiplier estimate; penalty parameter (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022622532499

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