Optimization with PDE Constraints

By Michael Hinze, René Pinnau, Michael Ulbrich, S. Ulbrich. Mathematical Modelling, 2008

1,455 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7907c090050e6bc6b6da65a181f0936d8c6e6b65

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

New regularity results and improved error estimates for optimal control problems with state constraints (2014, positive): “For the three dimensional case an improvement to h 3 4 is achieved in Rösch and Steinig [28] and an estimate of order h|log h| is shown in [21] for a problem with control and state constraints.”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “, [5, 26]), that is, equal to the number of parameters.”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, methodology): “[33] M.”
Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, methodology): “More specifically, the following proposition is a direct application of the adjoint method for the calculus of derivatives (see, e.g., Allaire 2007; Hinze et al. 2009).”
Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, neutral): “15); see [24, 26, 74].”
Optimization of wind plant layouts using an adjoint approach (2017, background): “Minimizing the reduced functional is equivalent to minimizing the original functional if the governing equations F produce a unique state u for a given set of controls m, and if F [u (m) ,m] is assumed to be continuously invertible so that u (m) is continuously differentiable (Hinze et al., 2009).”
Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters (2021, background): “Many problems in engineering and science, e.g., 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].”
Towards bridging the gap between motion capturing and biomechanical optimal control simulations (2015, background): “, its dynamics) as well as boundary conditions and path constraints, [8].”
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion (2013, neutral): “Here, inconsistency means that the former are equivalent to the latter only in the limit as the mesh size approaches zero (see also [26, 28]).”
Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation (2018, background): “For more details on these two approaches, we refer to [11].”