University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Divergences on symmetric cones and medians

Divergences on symmetric cones and medians

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

The motivation of this work is basically concerned with optimization methods for the L^2-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem).

On the other hand, the notion of fi delity plays an important role in quantum information theory and quantum computation. It has deep connections with quantum entanglement, quantum chaos, and quantum transitions. It also occurs in the context of the Wasserstein distance (or the Bures distance). Recently, a parameterized version of fi delity has been studied. It is called the sandwiched quasi-relative entropy.

In this talk, we introduce a parameterized version of fidelity on symmetric cones, namely sandwiched quasi-relative entropies, and construct a one-parameter family of divergences based on these entropies. We consider the median minimization problem of finite points over these divergences and establish existence and uniqueness of minimizer. Its global convergence rate analysis is provided according to the derived upper bound of the condition number of the Hessian function.

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

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