On the Existence of Affine Invariant Descent Directions

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• Florian Jarre (Heinrich-Heine-Universit\"at D\"usseldorf)
• Thursday 11 October 2018, 12:00-13:00
• Nuffield G13.

If you have a question about this talk, please contact Sergey Sergeev.

A prominent example of a polynomial time algorithmic scheme are interior-point methods for convex optimization. In this setting, affine invariance is crucial for the analysis. In this talk the existence of affine invariant descent directions for unconstrained minimization is discussed. While there may exist several affine invariant descent directions for smooth functions at a given point, there exists exactly one in the case of strictly convex quadratic functions and generally none in the case of quadratic functions with singular or indefinite Hessian. These results can be generalized to smooth nonlinear functions and have implications regarding the initialization of minimization algorithms. They stand in contrast to recent works on constrained convex and nonconvex optimization for which there may exist an affine invariant ``frame’’ that depends on the feasible set and that can be used to define an affine invariant descent direction.

Joint work with Yu-Hong Dai and Felix Lieder.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

This talk is included in these lists:

• Nuffield G13
• Optimisation and Numerical Analysis Seminars
• School of Mathematics events

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