On the worst-case performance of the optimization method of Cauchy for smooth strongly convex functions.

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• Etienne de Klerk (Technical University of Delft, the Netherlands)
• Monday 23 January 2017, 12:00-13:00
• Watson Building, B09 (The Sandbox).

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

We consider the Cauchy (or steepest descent) method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also give worst-case complexity bound for a noisy variant of gradient descent method. Finally, we show that these results may be applied to study the worst-case performance of Newton’s method for the minimization of self-concordant functions.

The proofs are computer-assisted, and rely on the resolution of semidefinite programming performance estimation problems as introduced in the paper [Y. Drori and M. Teboulle. Performance of first-order methods for smooth convex minimization: a novel approach. Mathematical Programming, 145(1-2):451-482, 2014].

Joint work with F. Glineur and A.B. Taylor.

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

This talk is included in these lists:

• Optimisation and Numerical Analysis Seminars
• School of Mathematics Events
• Watson Building, B09 (The Sandbox)

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