Kusch, Lisa; Albring, T.; Walther, A.; Gauger, N. R. A one-shot optimization framework with additional equality constraints applied to multi-objective aerodynamic shape optimization. (English) Zbl 1397.90360 Optim. Methods Softw. 33, No. 4-6, 694-707 (2018). Summary: This paper concerns the implementation and application of the extended one-shot approach including additional equality constraints to achieve a direct transition from simulation to optimization. The approach can be applied for different areas of scientific computing where partial differential equations are treated by using a fixed-point solver. The solver is extended in a semi-automated fashion. In a first step it is augmented with a consistent adjoint solver using algorithmic differentiation. Then the obtained reduced derivative information is directly employed to simultaneously achieve optimality and primal as well as adjoint feasibility. The methodology is implemented in the multi-physics package SU2 and applied for multi-objective aerodynamic shape optimization. Cited in 2 Documents MSC: 90C30 Nonlinear programming 65F08 Preconditioners for iterative methods 65K05 Numerical mathematical programming methods Keywords:one-shot optimization; automated optimal design; equality constraints; descent approach; algorithmic differentiation Software:dcc; SU2; CoDiPack; ADIC PDFBibTeX XMLCite \textit{L. Kusch} et al., Optim. Methods Softw. 33, No. 4--6, 694--707 (2018; Zbl 1397.90360) Full Text: DOI References: [1] Development of a consistent discrete adjoint solver in an evolving aerodynamic design framework, in 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics (AIAA), Dallas, TX, 2015 [2] Efficient aerodynamic design using the discrete adjoint method in SU2, in 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics (AIAA), Washington, 2016 [3] Albring, T.; Zhou, B.; Gauger, N.; Sagebaum, M., an aerodynamic design framework based on algorithmic differentiation, ERCOFTAC Bull., 102, 10-16, (2015) [4] Bischof, C. H.; Hovland, P. D.; Norris, B., on the implementation of automatic differentiation tools, Higher-Order Symbolic Comput., 21, 311-331, (2008) · Zbl 1168.65324 [5] Bosse, T., augmenting the one-shot framework by additional constraints, Optim. Methods Softw., 31, 1132-1148, (2016) · Zbl 1351.49041 [6] Bosse, T.; Gauger, N.; Griewank, A.; Günther, S.; Schulz, V., one-shot approaches to design optimzation, Internat. Ser. Numer. Math., 165, 43-66, (2014) · Zbl 1327.90300 [7] Semi-automatic transition from simulation to optimization, in Evolutionary and Deterministic Methods for Design, Optimization and Control: Applications to Industrial and Societal Problems - EUROGEN 2007, ISBN 978-84-96736-45-0, CIMNE, Barcelona, Spain, 2008 [8] Gauger, N.; Griewank, A.; Hamdi, A.; Kratzenstein, C.; Özkaya, E.; Slawig, T., automated extension of fixed point PDE solvers for optimal design with bounded retardation, Internat. Ser. Numer. Math., 106, 99-122, (2012) · Zbl 1356.49060 [9] Giles, M. B.; Pierce, N. A., an introduction to the adjoint approach to design, Flow Turbul. Combust., 65, 393-415, (2000) · Zbl 0996.76023 [10] Griewank, A.; Faure, C., reduced functions, gradients and hessians from fixed-point iterations for state equations, Numer. Algorithms, 30, 113-139, (2002) · Zbl 1005.65025 [11] Griewank, A.; Kressner, D., time-lag in derivative convergence for fixed point iterations, ARIMA Rev. Afr. Rech. Inform. Math. Appl., 3, 87-102, (2005) [12] Griewank, A.; Walther, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, (2008), Society for Industrial Mathematics · Zbl 1159.65026 [13] Hamdi, A.; Griewank, A., properties of an augmented Lagrangian for design optimization, Optim. Methods Softw., 25, 645-664, (2010) · Zbl 1225.90124 [14] Hamdi, A.; Griewank, A., reduced quasi-Newton method for simultaneous design and optimization, Comput. Optim. Appl., 49, 521-548, (2011) · Zbl 1251.90364 [15] Efficient calculation of Pareto-optimal points for shape optimization, in Full Paper Compilation: Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems - EUROGEN 2013, ISBN 978-84-617-2141-2, Universidad de Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain, 2014 [16] Lin, J. G., proper equality constraints and maximization of index vectors, J. Optim. Theory Appl., 20, 215-244, (1976) · Zbl 0314.90089 [17] Miettinen, K., Nonlinear Multiobjective Optimization, 12, (1999), Kluwer Academic Publishers, Dordrecht · Zbl 0949.90082 [18] Naumann, U., The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation, 24, (2012), SIAM, Philadelphia, PA · Zbl 1275.65015 [19] Özkaya, E.; Gauger, N. R., automatic transition from simulation to one-shot shape optimization with Navier–Stokes equations, GAMM-Mitt., 33, 133-147, (2010) · Zbl 1342.76068 [20] Stanford University Unstructured (SU2): An open-source integrated computational environment for multi-physics simulation and design, in 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, American Institute of Aeronautics and Astronautics (AIAA), Grapevine, TX, 2013, pp. 1–60 [21] Codipack – code differentiation package – scientific computing, 2017. Available at [22] Schmidt, S.; Ilic, C.; Schulz, V.; Gauger, N. R., three-dimensional large-scale aerodynamic shape optimization based on shape calculus, AIAA J., 51, 2615-2627, (2013) [23] Walther, A.; Gauger, N. R.; Kusch, L.; Richert, N., on an extension of one-shot methods to incorporate additional constraints, Optim. Methods Softw., 31, 494-510, (2016) · Zbl 1369.49041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.