Free Access
Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S13
Number of page(s) 31
DOI https://doi.org/10.1051/cocv/2020060
Published online 01 March 2021
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces. SIAM, Philadelphia (2006). [Google Scholar]
  3. H. Attouch, G. Garrigos and X. Goudou, A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions. J. Math. Anal. Appl. 422 (2015) 741–771. [Google Scholar]
  4. S. Banholzer, S. Beermann and S. Volkwein, POD-based bicriterial optimal control by the reference point method. 2nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2016. IFAC-PapersOnLine 49 (2016) 210–215. [Google Scholar]
  5. S. Banholzer and S. Volkwein, Hierarchical convex multiobjective optimization by the Euclidean reference point method. Preprint SPP1962-117 (2019). [Google Scholar]
  6. V. Barbu, Optimal Control of Variational Inequalities. Research Notes in Mathematics. Pitman (1984). [Google Scholar]
  7. D. Beermann, M. Dellnitz, S. Peitz and S. Volkwein, POD-based multiobjective optimal control of PDEs with non-smooth objectives. PAMM 17 (2017) 51–54. [Google Scholar]
  8. D. Beermann, M. Dellnitz, S. Peitz and S. Volkwein, Set-oriented multiobjective optimal control of PDEs using proper orthogonal decomposition, in Reduced-Order Modeling (ROM) for Simulation and Optimization: Powerful Algorithms as Key Enablers for Scientific Computing, edited by W. Keiper, A. Milde and S. Volkwein. Springer (2018) 47–72. [Google Scholar]
  9. S. Bellaassali and A. Jourani, Necessary optimality conditions in multiobjective dynamic optimization. SIAM J. Control Optim. 42 (2004) 2043–2061. [Google Scholar]
  10. J. Bienvenido and N. Vicente, Optimality conditions in directionally differentiable Pareto problems with a set constraint via tangent cones. Numer. Funct. Anal. Optim. 24 (2003) 557–574. [Google Scholar]
  11. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer, New York (2000). [Google Scholar]
  12. S.C. Brenner, Finite element methods for elliptic distributed optimal control problems with pointwise state constraints (survey), in Advances in Mathematical Sciences: AWM Research Symposium, Houston, TX, April 2019, edited by B. Acu, D. Danielli, M. Lewicka, A. Pati, R. V. Saraswathy and M. Teboh-Ewungkem. Springer (2020) 3–16. [Google Scholar]
  13. C. Christof, Sensitivity Analysis of Elliptic Variational Inequalities of the First and the Second Kind. Ph.D. thesis, Technische Universität Dortmund (2018). [Google Scholar]
  14. C. Christof, C. Meyer, S. Walther and C. Clason, Optimal control of a non-smooth semilinear elliptic equation. Math. Control Relat. Fields 8 (2018) 247–276. [Google Scholar]
  15. C. Christof and B. Vexler, New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints. To appear in: ESAIM: COCV (2020). Available from: https://doi.org/10.1051/cocv/2020059. [Google Scholar]
  16. C. Christof and G. Wachsmuth, On second-order optimality conditions for optimal control problems governed by the obstacle problem. To appear in: Optimization (2020). Available from: https://doi.org/10.1080/02331934.2020.1778686. [Google Scholar]
  17. F.H. Clarke, Optimization and Nonsmooth Analysis. SIAM’s Classics in Applied Mathematics. SIAM, Philadelphia, PA (1990). [Google Scholar]
  18. C. Clason, V.H. Nhu and A. Rösch, Optimal control of a non-smooth quasilinear elliptic equation. Preprint arXiv:1810.08007 (2018). [Google Scholar]
  19. J.C. De los Reyes and C. Meyer, Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the second kind. J. Optim. Theory Appl. 168 (2016) 375–409. [Google Scholar]
  20. S. Dempe. Foundations of Bilevel Programming. Vol. 61 of Nonconvex Optimization and Its Applications. Kluwer (2002). [Google Scholar]
  21. O. Ebel, S. Schmidt and A. Walther, Solving non-smooth semi-linear optimal control problems with abs-linearization. Preprint SPP1962-093 (2018). [Google Scholar]
  22. M. Ehrgott, Multicriteria Optimization, 2nd edn. Springer (2005). [Google Scholar]
  23. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland (1976). [Google Scholar]
  24. L.C. Evans, Partial Differential Equations, 2nd edn. AMS, Providence, RI (2010). [Google Scholar]
  25. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, reprint of the 1998 edn. Springer, Berlin/Heidelberg/New York (2001). [Google Scholar]
  26. G. Giorgi, B. Jiménez and V. Novo, On constraint qualifications in directionally differentiable multiobjective optimization problems. RAIRO: OR 38 (2004) 255–274. [Google Scholar]
  27. G. Giorgi, B. Jiménez and V. Novo, Strong Kuhn-Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems. TOP 17 (2008) 288–304. [Google Scholar]
  28. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman (1985). [Google Scholar]
  29. L. Iapichino, S. Ulbrich and S. Volkwein, Multiobjective PDE-constrained optimization using the reduced-basis method. Adv. Comput. Math. 43 (2017) 945–972. [Google Scholar]
  30. Y. Ishizuka, Optimality conditions for directionally differentiable multi-objective programming problems. J. Optim. Theory Appl. 72 (1992) 91–111. [Google Scholar]
  31. Y. Ishizuka and K. Shimizu, Necessary and sufficient conditions for the efficient solutions of nondifferentiable multiobjective problems. IEEE Trans. Syst. Man Cybernet. SMC-14 (1984) 625–629. [Google Scholar]
  32. B.N. Khoromskij and G. Wittum, Numerical Solution of Elliptic Differential Equations by Reduction to the Interface. Lecture Notes in Computational Science and Engineering. Springer, Berlin/Heidelberg (2012). [Google Scholar]
  33. F. Kikuchi, K. Nakazato and T. Ushijima, Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria. Japan J. Appl. Math. 1 (1984) 369–403. [Google Scholar]
  34. I.Y. Kim and O.L. de Weck, Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct. Multidiscip. Optim. 29 (2005) 149–158. [Google Scholar]
  35. Y.-B. Lü and W. Zhong-Ping, A smoothing method for solving bilevel multiobjective programming problems. J. Oper. Res. Soc. China 2 (2014) 511–525. [Google Scholar]
  36. M.M. Mäkelä, V.P. Eronen and N. Karmitsa, On nonsmooth multiobjective optimality conditions with generalized Convexities, in Optimization in Science and Engineering: In Honor of the 60th Birthday of Panos M. Pardalos, edited by T.M. Rassias, C.A. Floudas, and S. Butenko. Springer, New York, NY (2014) 333–357. [Google Scholar]
  37. O.L. Mangasarian, Nonlinear Programming. Vol 10 of SIAM’s Classics in Applied Mathematics, 2nd edn. SIAM (1994). [Google Scholar]
  38. C. Meyer and L. Susu, Optimal control of nonsmooth, semilinear parabolic equations. SIAM J. Control Optim. 55 (2017) 2206–2234. [Google Scholar]
  39. K.M. Miettinen, Nonlinear Multiobjective Optimization. Kluwer, Boston/London/Dordrecht (1999). [Google Scholar]
  40. F. Mignot, Contrôle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [Google Scholar]
  41. F. Mignot and J.P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466–476. [Google Scholar]
  42. B.S. Mordukhovich, Multiobjective optimization problems with equilibrium constraints. Math. Program. 117 (2009) 331–354. [Google Scholar]
  43. B.S. Mordukhovich, Variational Analysis and Applications. Springer Monographs in Mathematics. Springer (2018). [Google Scholar]
  44. S. Ober-Blöbaum and K. Padberg-Gehle, Multiobjective optimal control of fluid mixing. PAMM 15 (2015) 639–640. [Google Scholar]
  45. S. Peitz and M. Dellnitz, Gradient-based multiobjective optimization with uncertainties, in NEO 2016: Results of the Numerical and Evolutionary Optimization Workshop NEO 2016 and the NEO Cities 2016 Workshop held on September 20-24, 2016 in Tlalnepantla, Mexico, edited by Y. Maldonado, L. Trujillo, O. Schütze, A. Riccardi, and M. Vasile. Springer (2018) 159–182. [Google Scholar]
  46. S. Peitz and M. Dellnitz, A survey of recent trends in multiobjective optimal control - surrogate models, feedback control and objective reduction. Math. Comput. Appl. 23 (2018) 1–33. [Google Scholar]
  47. J. Rappaz, Approximation of a nondifferentiable nonlinear problem related to MHD equilibria. Numer. Math. 45 (1984) 117–133. [Google Scholar]
  48. A.-T. Rauls and S. Ulbrich, Computation of a Bouligand generalized derivative for the solution operator of the obstacle problem. SIAM J. Optim. 57 (2019) 3223–3248. [Google Scholar]
  49. A.-T. Rauls and G. Wachsmuth, Generalized derivatives for the solution operator of the obstacle problem. Set-Valued Var. Anal. (2019) 1–27. [Google Scholar]
  50. R.T. Rockafellar and R.J.-B. Wets, Variational analysis. Vol. 317 of Grundlehren der Mathematischen Wissenschaften. Springer (1998). [Google Scholar]
  51. M. Ruzicka, Nichtlineare Funktionalanalysis. Springer, Berlin/Heidelberg (2004). [Google Scholar]
  52. W. Schirotzek, Nonsmooth Analysis. Springer, Berlin/Heidelberg (2007). [Google Scholar]
  53. R. Temam, A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma. Arch. Rational Mech. Anal. 60 (1976) 51–73. [Google Scholar]
  54. A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, in Multiple Criteria Decision Making Theory and Application, edited by G. Fandel and T. Gal. Springer (1980) 468–486. [Google Scholar]
  55. J. Xin, An Introduction to Fronts in Random Media. Vol. 5 of Surveys and Tutorials in the Applied Mathematical Sciences. Springer (2009). [Google Scholar]
  56. J.J. Ye, Necessary optimality conditions for multiobjective bilevel programs. Math. Oper. Res. 36 (2011) 165–184. [Google Scholar]

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