1 Introduction; Kenneth Diest. 1.1 Introduction. 1.2 Ancient Metamaterials. 1.3 Modern Metamaterials. 1.4 Design. References.

2 An Overview of Mathematical Methods for Numerical Optimization; Daniel E. Marthaler. 2.1 Introduction. 2.2 Mathematical Optimization. 2.3 Finding Solutions. 2.4 Algorithms Utilizing Gradient Information. 2.5 Gradient Free Algorithms. 2.6 Summary. References.

3 Optimization with Surrogate Models; Tom Schaul . 3.1 Introduction. 3.2 Background. 3.3 Artificial Curiosity. 3.4 Exploration/Exploitation Trade-off. 3.5 Curiosity-driven Optimization. 3.6 Minimal Asymptotic Requirements. 3.7 Discussion. References.

4 Metamaterial Design by Mesh Adaptive Direct Search; Charles Audet, Kenneth Diest, Sébastien Le Digabel, Luke A. Sweatlock, and Daniel E. Marthaler. 4.1 Introduction. 4.2 The mesh adaptive direct search class of algorithms. 4.3 NOMAD: A C++ implementation of the MADS algorithm. 4.4 Metamaterial Design Using NOMAD. References.

5 Nature Inspired Optimization Techniques for Metamaterial Design; Douglas H. Werner, Jeremy A. Bossard, Zikri Bayraktar, Zhi Hao Jiang, Micah D. Gregory, and Pingjuan L. Werner. 5.1 Introduction. 5.2 Nature Inspired Optimization Methods. 5.3 Metamaterial Surface Optimization Examples. 5.4 Homogenized Metamaterial Optimization Examples. References.

6 Objective-First Nanophotonic Design; Jesse Lu and Jelena Vuckovic. 6.1 Introduction. 6.2 The Electromagnetic Wave Equation. 6.3 The Objective-first Design Problem. 6.4 Waveguide Coupler Design. 6.5 Optical Cloak Design. 6.6 Optical Mimic Design. 6.7 Extending the Method. 6.8 Conclusions. References.

7 Gradient Based Optimization Methods for Metamaterial Design; Weitao Chen, Kenneth Diest, Chiu-Yen Kao, Daniel E. Marthaler, Luke A. Sweatlock, and Stanley Osher. 7.1 Introduction. 7.2 Level Sets and Dynamic Implicit Surfaces. 7.3 Eigenfunction Optimization. References.

Appendix: The Interface Between Optimization and Simulation.