Optimizing Star-Convex Functions

@article{Lee2016OptimizingSF,
  title={Optimizing Star-Convex Functions},
  author={Jasper C. H. Lee and Paul Valiant},
  journal={2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2016},
  pages={603-614}
}
  • Jasper C. H. Lee, Paul Valiant
  • Published 2016
  • Mathematics, Computer Science
  • 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
Star-convexity is a significant relaxation of the notion of convexity, that allows for functions that do not have (sub)gradients at most points, and may even be discontinuous everywhere except at the global optimum. We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no Lipschitz or other smoothness assumptions whatsoever, and no restrictions except exponential boundedness on a region about the origin, and Lebesgue measurability. The algorithm's… Expand
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