Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penality parameters

Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penality parameters

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Article ID: iaor20001164
Country: Germany
Volume: 84
Issue: 1
Start Page Number: 161
End Page Number: 200
Publication Date: Jan 1999
Journal: Mathematical Programming
Authors: , ,
Abstract:

A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objective function and the constraints of the problem are only required to be differentiable and their gradients to satisfy a Lipschitz condition. The strategy for obtaining global convergence is based on the trust region approach. The merit function is a type of augmented Lagrangian. A new updating scheme is introduced by the penalty parameter, by means of which monotone increase is not necessary. Global convergence results are proved and numerical experiments are presented.

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