Open Access
Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 80 | |
Number of page(s) | 36 | |
DOI | https://doi.org/10.1051/cocv/2022070 | |
Published online | 23 December 2022 |
- R. Adams and J. Fournier, Sobolev Spaces, vol. 140. Elsevier (2003). [Google Scholar]
- A. Alexanderian, N. Petra, G. Stadler and O. Ghattas, Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations. SIAM/ASA J. Uncertainty Quantif. 5 (2017) 1166-1192. [CrossRef] [MathSciNet] [Google Scholar]
- J. Appell and P.P. Zabrejko, Vol. 95 of Nonlinear superposition operators. Cambridge University Press (1990). [Google Scholar]
- P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Coherent measures of risk. Math. Finance 9 (1999) 203-228. [Google Scholar]
- J.-P. Aubin and H. Frankowska, Set-valued analysis. Modern Birkhäuser Classics, Birkhäuser Boston Inc., Boston, MA (1990). [Google Scholar]
- J.M. Ball and F. Murat, Remarks on Chacon’s biting lemma. Proc. Am. Math. Soc. 107 (1989) 655-663. [Google Scholar]
- H.H. Bauschke, P.L. Combettes et al., Vol. 408 of Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer (2011). [Google Scholar]
- P. Benner, A. Onwunta and M. Stoll, Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. SIAM J. Matrix Anal. Appi. 37 (2016) 491-518. [CrossRef] [Google Scholar]
- M. Bergounioux and F. Troltzsch, Optimal control of linear bottleneck problems. ESAIM: COCV 3 (1998) 235-250. [CrossRef] [EDP Sciences] [Google Scholar]
- J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer-Verlag, New York (2013). [Google Scholar]
- E. Casas, Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 24 (1986) 1309-1318. [CrossRef] [MathSciNet] [Google Scholar]
- P. Chen and O. Ghattas, Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters. SIAM/ASA J. Uncert. Quantif. 9 (2021) 1381-1410. [CrossRef] [Google Scholar]
- P. Chen, A. Quarteroni and G. Rozza, A weighted reduced basis method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 51 (2013) 3163-3185. [CrossRef] [MathSciNet] [Google Scholar]
- S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Shape optimization under uncertainty-a stochastic programming perspective. SIAM J. Optim. 19 (2008) 1610-1632. [Google Scholar]
- D. Dentcheva and A. Ruszczynski, Subregular recourse in nonlinear multistage stochastic optimization. Math. Program. (2021) 1-22. [Google Scholar]
- Y. Ermoliev, T. Ermolieva, T. Kahil, M. Obersteiner, V. Gorbachuk and P. Knopov, Stochastic optimization models for risk-based reservoir management. Cybern. Syst. Anal. 55 (2019) 55-64. [CrossRef] [Google Scholar]
- M.H. Farshbaf-Shaker, R. Henrion and D. Hömberg, Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization. Set-Valued Variat. Anal. 26 (2018) 821-841. [CrossRef] [Google Scholar]
- D. Filipović and G. Svindland, The canonical model space for law-invariant convex risk measures is L1. Math. Finance 22 (2012) 585-589. [CrossRef] [MathSciNet] [Google Scholar]
- D.B. Gahururu, M. Hintermüller and T.M. Surowiec, Risk-neutral PDE-constrained generalized Nash equilibrium problems. Math. Program. (2022) 1-51. [Google Scholar]
- C. Geiersbach and W. Wollner, A stochastic gradient method with mesh refinement for PDE-constrained optimization under uncertainty. SIAM J. Scient. Comput. 42 (2020) A2750-A2772. [CrossRef] [Google Scholar]
- C. Geiersbach and W. Wollner, Optimality conditions for convex stochastic optimization problems in banach spaces with almost sure state constraints. SIAM J. Optim. 4 (2021) 2455-2480. [CrossRef] [MathSciNet] [Google Scholar]
- A. Geletu, A. Hoffmann, P. Schmidt and P. Li, Chance constrained optimization of elliptic PDE systems with a smoothing convex approximation. ESAIM: COCV 26 (2020) 70. [CrossRef] [EDP Sciences] [Google Scholar]
- M. Hintermuäller and K. Kunisch, Feasible and noninterior path-following in constrained minimization with low multiplier regularity. SIAM J. Control Optim. 45 (2006) 1198-1221. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hintermuäller and K. Kunisch, Path-following methods for a class of constrained minimization problems in function space. SIAM J. Optim. 17 (2006) 159-187. [CrossRef] [MathSciNet] [Google Scholar]
- A.D. Ioffe and V.L. Levin, Subdifferentials of convex functions. Trudy Moskovskogo Matematicheskogo Obshchestva 26 (1972) 3-73. [Google Scholar]
- P. Kolvenbach, O. Lass and S. Ulbrich, An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty. Optim. Eng. 19 (2018) 697-731. [CrossRef] [MathSciNet] [Google Scholar]
- D.P. Kouri, M. Heinkenschloss, D. Ridzal and B.G. van Bloemen Waanders, A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty. SIAM J. Sci. Comput. 35 (2013) A1847-A1879. [CrossRef] [Google Scholar]
- D.P. Kouri and T.M. Surowiec, Risk-averse PDE-constrained optimization using the conditional value-at-risk. SIAM J. Optim. 26 (2016) 365-396. [Google Scholar]
- D.P. Kouri and T.M. Surowiec, Existence and optimality conditions for risk-averse PDE-constrained optimization. SIAM/ASA J. Uncertainty Quant. 6 (2018) 787-815. [CrossRef] [Google Scholar]
- V.L. Levin, The Lebesgue decomposition for functionals on the vector-function space LX. Funct. Anal. Appi. 8 (1974) 314-317. [Google Scholar]
- J.M. Mulvey and B. Shetty, Financial planning via multi-stage stochastic optimization. Comput. Oper. Res. 31 (2004) 1-20. [CrossRef] [MathSciNet] [Google Scholar]
- M.V. Pereira and L.M. Pinto, Multi-stage stochastic optimization applied to energy planning. Math. Program. 52 (1991) 359-375. [CrossRef] [Google Scholar]
- G. Pflug and A. Pichler, Multistage Stochastic Optimization, Springer (2014). [Google Scholar]
- G. Pflug and W. Römisch, Modeling, Measuring and Managing Risk. World Scientific (2007). [Google Scholar]
- R. Rockafellar, Integrals which are convex functionals. II. Pacific J. Math. 39 (1971) 439-469. [CrossRef] [MathSciNet] [Google Scholar]
- R.T. Rockafellar, Convex integral functionals and duality, in Contributions to nonlinear functional analysis. Elsevier (1971), pp. 215-236. [Google Scholar]
- R.T. Rockafellar, Conjugate duality and optimization. SIAM (1974). 10.1137/1.9781611970524. [Google Scholar]
- R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, in Nonlinear operators and the calculus of variations. Springer (1976), pp. 157-207. [Google Scholar]
- R.T. Rockafellar and J. Royset, Engineering decisions under risk averseness. ASCE-ASME J. Risk Uncert. Eng. Syst. A 1 (2015) 04015003. [CrossRef] [Google Scholar]
- R.T. Rockafellar and R.J.-B. Wets, Stochastic convex programming: Kuhn-Tucker conditions. J. Math. Econ. 2 (1975) 349-370. [CrossRef] [Google Scholar]
- R.T. Rockafellar and R.J.-B. Wets, Stochastic convex programming: basic duality. Pacific J. Math. 62 (1976) 173-195. [CrossRef] [MathSciNet] [Google Scholar]
- R.T. Rockafellar and R.J.-B. Wets, Stochastic convex programming: relatively complete recourse and induced feasibility. SIAM J. Control Optim. 14 (1976) 574-589. [CrossRef] [MathSciNet] [Google Scholar]
- R.T. Rockafellar and R.J.-B. Wets, Stochastic convex programming: singular multipliers and extended duality singular multipliers and duality. Pacific J. Math. 62 (1976) 507-522. [CrossRef] [MathSciNet] [Google Scholar]
- C. Schillings, S. Schmidt and V. Schulz, Efficient shape optimization for certain and uncertain aerodynamic design. Comput. Fluids 46 (2011) 78-87. [CrossRef] [MathSciNet] [Google Scholar]
- A. Shapiro, D. Dentcheva and A. Ruszczyński, Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia (2009). [Google Scholar]
- J.J. Uhl, Extensions and decompositions of vector measures. J. London Math. Soc. 2 (1971) 672-676. [CrossRef] [Google Scholar]
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