In non-convex optimisations our ultimate destination depends upon the starting point.
- Zeyuan ALLEN-ZHU: Recent Advances in Stochastic Convex and Non-Convex Optimization. Clear, has good pointers.
With symmetries
Zhang, Qu, and Wright (2022)
In phase retrieval
See phase retrieval.
References
Choromanska, Anna, MIkael Henaff, Michael Mathieu, Gerard Ben Arous, and Yann LeCun. 2015. “The Loss Surfaces of Multilayer Networks.” In Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, 192–204.
Jain, Prateek, and Purushottam Kar. 2017. Non-Convex Optimization for Machine Learning. Vol. 10.
Soltanolkotabi, M., A. Javanmard, and J. D. Lee. 2019. “Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks.” IEEE Transactions on Information Theory 65 (2): 742–69.
Wright, John, and Yi Ma. 2022. High-dimensional data analysis with low-dimensional models: Principles, computation, and applications. S.l.: Cambridge University Press.
Zhang, Yuqian, Qing Qu, and John Wright. 2022. “From Symmetry to Geometry: Tractable Nonconvex Problems.” arXiv.
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