A multilevel, level-set method for optimizing eigenvalues in shape design problems

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A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “Finally, Haber (2004) used a sequential quadratic programming (SQP) method in conjunction with multilevel continuation schemes to advance the implicit shape boundary rather than solving the Hamilton-Jacobi PDE.”
A level set‐based parameterization method for structural shape and topology optimization (2008, methodology): “Due to these reasons, in continuum shape and topology optimization, it has been substantiated that the convergence of conventional level set methods to reach the optimal design is slow and the design is easy to run into a local minimum [27, 32].”
Level set methods for inverse scattering (2006, background): “Another example is the optimization of a band-gap structure or of maximal eigenvalues [77, 91, 123].”
A survey on level set methods for inverse problems and optimal design (2005, methodology): “Model problem 4 is a simplified version of this problem, it has been treated by a level set based projected gradient method in Osher & Santosa [108] (see Figure 1 for an illustration of results), and by a Gauss-Newton type approach using approximate eigenvalue calculations in Haber [64].”