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Summary: Tech. Report UCL-INMA-2009.024
All roads lead to Newton: Feasible second-order methods for
equality-constrained optimization
P.-A. Absil
Jochen Trumpf
Robert Mahony
Ben Andrews§
August 31, 2009
Abstract
This paper considers the connection between the intrinsic Riemannian
Newton method and other more classically inspired optimization algo-
rithms for equality-constrained optimization problems. We consider the
feasibly-projected sequential quadratic programming (FP-SQP) method
and show that it yields the same update step as the Riemannian Newton,
subject to a minor assumption on the choice of multiplier vector. We
also consider Newton update steps computed in various `natural' local
coordinate systems on the constraint manifold and find simple condi-
tions that guarantee that the update step is the Riemannian Newton
update. In particular, we show that this is the case for projective local
coordinates, one of the most natural choices that have been proposed in
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