Optimizing Fusion Simulations with Some Available Derivatives
Abstract: In the taxonomy of optimization problems, derivative-based methods can typically be used only when the full gradient of the objective function is available. However, for some objectives, the full gradient may not be available, but some components are.
In this talk, we describe an extension to derivative-free optimization algorithms that takes advantage of the limited available derivative information in this scenario. We present a trust-region algorithm with objective function models based on Hermite interpolation. The method reduces to the classical derivative-free method with models based on Lagrange interpolation when no derivatives are available.
We analyze the convergence properties of this algorithm, and demonstrate numerical performance both on synthetic problems and on applications within the magnetic confinement fusion community.
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