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On an Approximation of the Hessian of the Lagrangian

Florian Jarre (jarre***at***opt.uni-duesseldorf.de)

Abstract: In the context of SQP methods or, more recently, of sequential semidefinite programming methods, it is common practice to construct a positive semidefinite approximation of the Hessian of the Lagrangian. The Hessian of the augmented Lagrangian is a suitable approximation as it maintains local superlinear convergence under appropriate assumptions. In this note we give a simple example that the orthogonal projection of the Hessian of the Lagrangian onto the cone of semidefinite matrices may lead to arbitrarily slow local convergence, and is thus not a suitable approximation.

Keywords: SQP method, Lagrangian, approximate Hessian.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Optimization Software and Modeling Systems (Optimization Software Design Principles )

Citation: unpublished

Download: [Postscript][Compressed Postscript][PDF]

Entry Submitted: 12/17/2003
Entry Accepted: 12/17/2003
Entry Last Modified: 12/17/2003

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