# Efficient Sampling from Feasible Sets of SDPs and Volume Approximation

@article{Chalkis2020EfficientSF, title={Efficient Sampling from Feasible Sets of SDPs and Volume Approximation}, author={Apostolos Chalkis and Ioannis Z. Emiris and Vissarion Fisikopoulos and Panagiotis Repouskos and Elias P. Tsigaridas}, journal={ArXiv}, year={2020}, volume={abs/2010.03817} }

We present algorithmic, complexity, and implementation results on the problem of sampling points from a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is geometric random walks. We analyze the arithmetic and bit complexity of certain primitive geometric operations that are based on the algebraic properties of spectrahedra and the polynomial eigenvalue problem. This study leads to the implementation of a broad collection of random walks for sampling from…

## One Citation

### A Cutting-plane Method for Semidefinite Programming with Potential Applications on Noisy Quantum Devices

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- 2021

It is shown how to leverage quantum speed-up of an eigensolver in speeding up an SDP solver utilizing the cutting-plane method, and that the RCP method is very robust to noise in the boundary oracle, which may make RCP suitable for use even on noisy quantum devices.

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