On an Approximation of the Hessian of the Lagrangian
Florian Jarre (jarreopt.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 )
Entry Submitted: 12/17/2003
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