Geiersbach, Caroline; Loayza-Romero, Estefania; Welker, Kathrin Stochastic approximation for optimization in shape spaces. (English) Zbl 07304308 SIAM J. Optim. 31, No. 1, 348-376 (2021). Reviewer: Antoine Henrot (Vandœuvre-lès-Nancy) MSC: 49Q10 35R60 60H15 60H30 60H35 35R15 PDF BibTeX XML Cite \textit{C. Geiersbach} et al., SIAM J. Optim. 31, No. 1, 348--376 (2021; Zbl 07304308) Full Text: DOI
Doganay, O. T.; Gottschalk, H.; Hahn, C.; Klamroth, K.; Schultes, J.; Stiglmayr, M. Gradient based biobjective shape optimization to improve reliability and cost of ceramic components. (English) Zbl 1452.74095 Optim. Eng. 21, No. 4, 1359-1387 (2020). MSC: 74P10 49Q10 60G55 90B25 PDF BibTeX XML Cite \textit{O. T. Doganay} et al., Optim. Eng. 21, No. 4, 1359--1387 (2020; Zbl 1452.74095) Full Text: DOI
Martínez-Frutos, Jesús; Herrero-Pérez, David; Kessler, Mathieu; Periago, Francisco Risk-averse structural topology optimization under random fields using stochastic expansion methods. (English) Zbl 1439.74292 Comput. Methods Appl. Mech. Eng. 330, 180-206 (2018). MSC: 74P15 60G60 74S60 PDF BibTeX XML Cite \textit{J. Martínez-Frutos} et al., Comput. Methods Appl. Mech. Eng. 330, 180--206 (2018; Zbl 1439.74292) Full Text: DOI
Conti, Sergio; Rumpf, Martin; Schultz, Rüdiger; Tölkes, Sascha Stochastic dominance constraints in elastic shape optimization. (English) Zbl 1417.35214 SIAM J. Control Optim. 56, No. 4, 3021-3034 (2018). Reviewer: Baasansuren Jadamba (Rochester) MSC: 35Q93 49Q10 65N30 74M05 93C20 65N50 PDF BibTeX XML Cite \textit{S. Conti} et al., SIAM J. Control Optim. 56, No. 4, 3021--3034 (2018; Zbl 1417.35214) Full Text: DOI
Thore, Carl-Johan; Holmberg, Erik; Klarbring, Anders A general framework for robust topology optimization under load-uncertainty including stress constraints. (English) Zbl 1439.74296 Comput. Methods Appl. Mech. Eng. 319, 1-18 (2017). MSC: 74P15 PDF BibTeX XML Cite \textit{C.-J. Thore} et al., Comput. Methods Appl. Mech. Eng. 319, 1--18 (2017; Zbl 1439.74296) Full Text: DOI
Chen, Ning; Yu, Dejie; Xia, Baizhan; Ma, Zhengdong Topology optimization of structures with interval random parameters. (English) Zbl 1436.74054 Comput. Methods Appl. Mech. Eng. 307, 300-315 (2016). MSC: 74P15 74P10 PDF BibTeX XML Cite \textit{N. Chen} et al., Comput. Methods Appl. Mech. Eng. 307, 300--315 (2016; Zbl 1436.74054) Full Text: DOI
Martínez-Frutos, Jesús; Herrero-Pérez, David; Kessler, Mathieu; Periago, Francisco Robust shape optimization of continuous structures via the level set method. (English) Zbl 1425.74386 Comput. Methods Appl. Mech. Eng. 305, 271-291 (2016). MSC: 74P20 74B05 49Q10 65C30 PDF BibTeX XML Cite \textit{J. Martínez-Frutos} et al., Comput. Methods Appl. Mech. Eng. 305, 271--291 (2016; Zbl 1425.74386) Full Text: DOI
Koutsourelakis, P. S. Variational Bayesian strategies for high-dimensional, stochastic design problems. (English) Zbl 1351.62073 J. Comput. Phys. 308, 124-152 (2016). MSC: 62F15 62F10 65C50 PDF BibTeX XML Cite \textit{P. S. Koutsourelakis}, J. Comput. Phys. 308, 124--152 (2016; Zbl 1351.62073) Full Text: DOI arXiv
Allaire, Grégoire; Dapogny, Charles A deterministic approximation method in shape optimization under random uncertainties. (English) Zbl 1416.74080 SMAI J. Comput. Math. 1, 83-143 (2015). MSC: 74P20 49Q10 65K10 90C15 65C20 74S30 PDF BibTeX XML Cite \textit{G. Allaire} and \textit{C. Dapogny}, SMAI J. Comput. Math. 1, 83--143 (2015; Zbl 1416.74080) Full Text: DOI
Carrasco, Miguel; Ivorra, Benjamin; Ramos, Angel Manuel Stochastic topology design optimization for continuous elastic materials. (English) Zbl 1423.74727 Comput. Methods Appl. Mech. Eng. 289, 131-154 (2015). MSC: 74P05 35Q74 74P15 74B05 74S60 74S05 PDF BibTeX XML Cite \textit{M. Carrasco} et al., Comput. Methods Appl. Mech. Eng. 289, 131--154 (2015; Zbl 1423.74727) Full Text: DOI
Dambrine, Marc; Dapogny, Charles; Harbrecht, Helmut Shape optimization for quadratic functionals and states with random right-hand sides. (English) Zbl 1326.49070 SIAM J. Control Optim. 53, No. 5, 3081-3103 (2015). MSC: 49Q10 49J55 49M30 60H35 65N75 PDF BibTeX XML Cite \textit{M. Dambrine} et al., SIAM J. Control Optim. 53, No. 5, 3081--3103 (2015; Zbl 1326.49070) Full Text: DOI
Martínez-Frutos, Jesús; Kessler, Mathieu; Periago, Francisco Robust optimal shape design for an elliptic PDE with uncertainty in its input data. (English) Zbl 1323.49029 ESAIM, Control Optim. Calc. Var. 21, No. 4, 901-923 (2015). MSC: 49Q10 49J55 49J20 49M20 93E20 35R60 35J20 60H15 65K10 60G60 60G15 PDF BibTeX XML Cite \textit{J. Martínez-Frutos} et al., ESAIM, Control Optim. Calc. Var. 21, No. 4, 901--923 (2015; Zbl 1323.49029) Full Text: DOI
Zhao, Junpeng; Wang, Chunjie Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices. (English) Zbl 1296.74085 Comput. Methods Appl. Mech. Eng. 273, 204-218 (2014). MSC: 74P15 PDF BibTeX XML Cite \textit{J. Zhao} and \textit{C. Wang}, Comput. Methods Appl. Mech. Eng. 273, 204--218 (2014; Zbl 1296.74085) Full Text: DOI
Allaire, Grégoire; Dapogny, Charles A linearized approach to worst-case design in parametric and geometric shape optimization. (English) Zbl 1297.49075 Math. Models Methods Appl. Sci. 24, No. 11, 2199-2257 (2014). MSC: 49Q10 49J20 65K05 74P20 90C90 PDF BibTeX XML Cite \textit{G. Allaire} and \textit{C. Dapogny}, Math. Models Methods Appl. Sci. 24, No. 11, 2199--2257 (2014; Zbl 1297.49075) Full Text: DOI
Geihe, Benedict; Lenz, Martin; Rumpf, Martin; Schultz, Rüdiger Risk averse elastic shape optimization with parametrized fine scale geometry. (English) Zbl 1280.90090 Math. Program. 141, No. 1-2 (A), 383-403 (2013). MSC: 90C15 65N38 65K10 PDF BibTeX XML Cite \textit{B. Geihe} et al., Math. Program. 141, No. 1--2 (A), 383--403 (2013; Zbl 1280.90090) Full Text: DOI
Atwal, Pradeep; Conti, Sergio; Geihe, Benedict; Pach, Martin; Rumpf, Martin; Schultz, Rüdiger On shape optimization with stochastic loadings. (English) Zbl 1356.93094 Leugering, Günter (ed.) et al., Constrained optimization and optimal control for partial differential equations. Basel: Birkhäuser (ISBN 978-3-0348-0132-4/hbk; 978-3-0348-0133-1/ebook). ISNM. International Series of Numerical Mathematics 160, 215-243 (2012). MSC: 93E20 90C15 74B05 65N30 65N38 34F05 49K45 PDF BibTeX XML Cite \textit{P. Atwal} et al., ISNM, Int. Ser. Numer. Math. 160, 215--243 (2012; Zbl 1356.93094) Full Text: DOI
Brittain, Kevin; Silva, Mariana; Tortorelli, Daniel A. Minmax topology optimization. (English) Zbl 1274.74320 Struct. Multidiscip. Optim. 45, No. 5, 657-668 (2012). MSC: 74P15 74Q05 49Q12 74A50 PDF BibTeX XML Cite \textit{K. Brittain} et al., Struct. Multidiscip. Optim. 45, No. 5, 657--668 (2012; Zbl 1274.74320) Full Text: DOI
Patel, Jiten; Choi, Seung-Kyum Classification approach for reliability-based topology optimization using probabilistic neural networks. (English) Zbl 1274.74376 Struct. Multidiscip. Optim. 45, No. 4, 529-543 (2012). MSC: 74P15 PDF BibTeX XML Cite \textit{J. Patel} and \textit{S.-K. Choi}, Struct. Multidiscip. Optim. 45, No. 4, 529--543 (2012; Zbl 1274.74376) Full Text: DOI
Tootkaboni, Mazdak; Asadpoure, Alireza; Guest, James K. Topology optimization of continuum structures under uncertainty - A polynomial chaos approach. (English) Zbl 1239.74081 Comput. Methods Appl. Mech. Eng. 201-204, 263-275 (2012). MSC: 74P15 74S60 65N30 65N75 PDF BibTeX XML Cite \textit{M. Tootkaboni} et al., Comput. Methods Appl. Mech. Eng. 201--204, 263--275 (2012; Zbl 1239.74081) Full Text: DOI
Takezawa, Akihiro; Nii, Satoru; Kitamura, Mitsuru; Kogiso, Nozomu Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system. (English) Zbl 1230.74155 Comput. Methods Appl. Mech. Eng. 200, No. 25-28, 2268-2281 (2011). MSC: 74P15 74S05 PDF BibTeX XML Cite \textit{A. Takezawa} et al., Comput. Methods Appl. Mech. Eng. 200, No. 25--28, 2268--2281 (2011; Zbl 1230.74155) Full Text: DOI
Chen, Shikui; Chen, Wei; Lee, Sanghoon Level set based robust shape and topology optimization under random field uncertainties. (English) Zbl 1274.74323 Struct. Multidiscip. Optim. 41, No. 4, 507-524 (2010). MSC: 74P15 49Q10 93D09 PDF BibTeX XML Cite \textit{S. Chen} et al., Struct. Multidiscip. Optim. 41, No. 4, 507--524 (2010; Zbl 1274.74323) Full Text: DOI
Žampachová, Eva; Popela, Pavel; Mrázek, Michal Optimum beam design via stochastic programming. (English) Zbl 1201.90145 Kybernetika 46, No. 3, 571-582 (2010). MSC: 90C15 65C05 90C29 49M27 PDF BibTeX XML Cite \textit{E. Žampachová} et al., Kybernetika 46, No. 3, 571--582 (2010; Zbl 1201.90145) Full Text: Link EuDML