The gradient descent/ascent method is a classical approach to find the minimum/maximum of an objective function or functional based on a first-order approximation. The method works in spaces of any number of dimensions, even in infinite-dimensional spaces. This method can converge more efficiently than methods which do not require derivative information; however, in certain circumstances the “cost function space” may become discontinuous and as a result, the derivatives may be difficult or impossible to determine. Here, we discuss both level set methods and eigenfunction optimization for representing the topography of a dielectric environment and efficient techniques for using gradient methods to solve different material design problems. Numerous results are shown to demonstrate the robustness of the gradient-based approach.
CITATION STYLE
Chen, W., Diest, K., Kao, C. Y., Marthaler, D. E., Sweatlock, L. A., & Osher, S. (2013). Gradient Based Optimization Methods for Metamaterial Design. In Topics in Applied Physics (Vol. 127, pp. 175–204). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-94-007-6664-8_7
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