Computational Optimization of Systems Governed by Partial Differential Equations

By Alfio Borzì, Volker H. Schulz. Computational science and engineering, 2012

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Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters (2021, background): “, shape optimization in aerodynamics or heat transfer in thermal conduction problems, deal with optimization problems constrained by partial differential equations (PDEs) [8,13,25,27,34].”
Full-waveform inversion in three-dimensional PML-truncated elastic media (2015, background): “With this definition, it is not possible to talk about the gradient, without specifying the inner-product utilized to represent the derivative [43].”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, methodology): “A possible future application of deflation is to the computation of multiple local optima of PDE-constrained optimisation problems, possibly with additional equality constraints [33, 10], by means of computing distinct solutions of the associated Karush–Kuhn–Tucker equations.”