Milz, Johannes; Ulbrich, Michael An approximation scheme for distributionally robust PDE-constrained optimization. (English) Zbl 1493.90120 SIAM J. Control Optim. 60, No. 3, 1410-1435 (2022). MSC: 90C17 90C26 90C59 65K05 PDF BibTeX XML Cite \textit{J. Milz} and \textit{M. Ulbrich}, SIAM J. Control Optim. 60, No. 3, 1410--1435 (2022; Zbl 1493.90120) Full Text: DOI OpenURL
Martínez-Frutos, J.; Ortigosa, R. Risk-averse approach for topology optimization of fail-safe structures using the level-set method. (English) Zbl 1487.74104 Comput. Mech. 68, No. 5, 1039-1061 (2021). Reviewer: Dimitris P. Vartziotis (Ioannina) MSC: 74P15 74K99 74S99 PDF BibTeX XML Cite \textit{J. Martínez-Frutos} and \textit{R. Ortigosa}, Comput. Mech. 68, No. 5, 1039--1061 (2021; Zbl 1487.74104) Full Text: DOI OpenURL
Chen, Peng; Ghattas, Omar Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters. (English) Zbl 1473.65072 SIAM/ASA J. Uncertain. Quantif. 9, 1381-1410 (2021). MSC: 65K10 49J55 49M41 65D32 65N12 93E20 PDF BibTeX XML Cite \textit{P. Chen} and \textit{O. Ghattas}, SIAM/ASA J. Uncertain. Quantif. 9, 1381--1410 (2021; Zbl 1473.65072) Full Text: DOI arXiv OpenURL
Geiersbach, Caroline; Wollner, Winnifried Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraints. (English) Zbl 1484.90055 SIAM J. Optim. 31, No. 4, 2455-2480 (2021). Reviewer: Kurt Marti (München) MSC: 90C15 49K99 49N15 PDF BibTeX XML Cite \textit{C. Geiersbach} and \textit{W. Wollner}, SIAM J. Optim. 31, No. 4, 2455--2480 (2021; Zbl 1484.90055) Full Text: DOI arXiv OpenURL
Geiersbach, Caroline; Loayza-Romero, Estefania; Welker, Kathrin Stochastic approximation for optimization in shape spaces. (English) Zbl 1458.49034 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 1458.49034) Full Text: DOI arXiv OpenURL
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 arXiv OpenURL
Yin, Shengwen; Chen, Ning; Yu, Dejie; Ma, Zhengdong Microstructural topology optimization for minimizing the sound pressure level of structural-acoustic coupled systems with multi-scale random parameters. (English) Zbl 07637037 Eng. Optim. 51, No. 7, 1185-1206 (2019). MSC: 90-XX PDF BibTeX XML Cite \textit{S. Yin} et al., Eng. Optim. 51, No. 7, 1185--1206 (2019; Zbl 07637037) Full Text: DOI OpenURL
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 OpenURL
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 arXiv OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 Link OpenURL
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 arXiv OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 OpenURL
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 Link OpenURL
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 OpenURL
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 OpenURL
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 Link OpenURL
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 OpenURL
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: EuDML Link OpenURL