Interval arithmetic provides a way to perform computations with continuous sets of real numbers or vectors, for example to bound the range of a function over a given set.

This can be used to find roots (zeros) of functions in a guaranteed way, by excluding regions where there are no roots and zooming in on roots, but always within a given interval.

It can also be used to do global optimization of functions in a deterministic way, that is, find the global minimum of a non-convex, nonlinear function. Interval methods for global optimization provide a guaranteed bound for the global optimum, and sets that contain the optimizers.

This project proposes to significantly improve these methods using techniques found in the interval arithmetic literature.

Organization

Student

Eeshan Gupta

Mentors

  • Mike Innes
  • Dpsanders
  • Christopher Rackauckas
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2018