References
- Kikuchi F, Nakazato K, Ushijima T. Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria. Japan J Appl Math. 1984;1(2):369–403.
- Temam R. A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma. Arch Ration Mech Anal. 1975/76;60(1):51–73.
- Rappaz J. Approximation of a nondifferentiable nonlinear problem related to MHD equilibria. Numer Math. 1984;45(1):117–133.
- Christof C, Clason C, Meyer C, et al. Optimal control of a non-smooth semilinear elliptic equation. Math Control Relat Fields. 2018;8(1):247–276.
- Casas E, Mateos M. Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J Control Optim. 2002;40(5):1431–1454.
- Casas E, Dhamo V. Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations. Control Cybernet. 2011;40(2):457–490.
- Casas E. Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints. ESAIM: Control Optim Calc Var. 2008;14(3):575–589.
- Krumbiegel K, Neitzel I, Rösch A. Sufficient optimality conditions for the Moreau–Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints. Ann Acad Rom Sci Ser Math Appl. 2010;2(2):222–246.
- Rösch A, Tröltzsch F. Sufficient second-order optimality conditions for an elliptic optimal control problem with pointwise control-state constraints. SIAM J Optim. 2006;17(3):776–794.
- Rösch A, Tröltzsch F. Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise control-state constraints. SIAM J Control Optim. 2003;42(1):138–154.
- Tröltzsch F. Optimal control of partial differential equations: theory, methods and applications. Providence (RI): American Mathematical Society; 2010. (Graduate studies in mathematics; vol. 112). Translated from the 2005 German original by Jürgen Sprekels.
- Casas E, Tröltzsch F. Second order optimality conditions and their role in PDE control. Jahresber Dtsch Math-Ver. 2015;117(1):3–44.
- Kunisch K, Wachsmuth D. Sufficient optimality conditions and semi-smooth Newton methods for optimal control of stationary variational inequalities. ESAIM: Control Optim Calc Var. 2012;18(2):520–547.
- Betz LM. Second-order sufficient optimality conditions for optimal control of nonsmooth, semilinear parabolic equations. SIAM J Control Optim. 2019;57(6):4033–4062.
- Christof C, Wachsmuth G. On second-order optimality conditions for optimal control problems governed by the obstacle problems. Optimization. 2020:1–41. (Advance online publication).
- Clason C, Nhu VH, Rösch A. No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation. ESAIM: Control Optim Calc Var. 2020; (Advance online publication). DOI:10.1051/cocv/2020092
- Betz T, Meyer C. Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening. ESAIM: Control Optim Calc Var. 2015;21(1):271–300.
- Wachsmuth G, Wachsmuth D. Convergence and regularization results for optimal control problems with sparsity functional. ESAIM: Control Optim Calc Var. 2011;17:858–886.
- Wachsmuth G, Wachsmuth D. Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints. Control Cybernet. 2011;40:1125–1158.
- Wachsmuth D. Adaptive regularization and discretization of bang-bang optimal control problems. Electron Trans Numer Anal. 2013;40:249–267.
- Deckelnick K, Hinze M. A note on the approximation of elliptic control problems with bang-bang controls. Comput Optim Appl. 2012;51:931–939.
- Christof C, Wachsmuth G. No-gap second-order conditions via a directional curvature functional. SIAM J Optim. 2018;28(3):2097–2130.
- Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. Berlin, Heidelberg: Springer-Verlag; 2000.
- Clason C, Nhu VH. Bouligand–Landweber iteration for a non-smooth ill-posed problem. Numer Math. 2019;142:789–832.
- Casas E, Tröltzsch F. First- and second-order optimality conditions for a class of optimal control problems with quasilinear elliptic equations. SIAM J Control Optim. 2009;48(2):688–718.
- Chipot M. Elliptic equations: an introductory course. Basel: Birkhäuser Verlag; 2009.
- Clason C, Nhu VH, Rösch A. Optimal control of a non-smooth quasilinear elliptic equation. Math Control Relat Fields. 2018;11(3):521–554.
- Barbu V. Optimal control of variational inequalities. Boston: Pitman (Advanced Publishing Program); 1984. (Research notes in mathematics; vol. 100).
- Meyer C, Susu LM. Optimal control of nonsmooth, semilinear parabolic equations. SIAM J Control Optim. 2017;55(4):2206–2234.
- Christof C, Müller G. Multiobjective optimal control of a non-smooth semilinear elliptic partial differential equation. ESAIM: Control Optim Calc Var. 2020;27:31.
- Bayen T, Bonnans JF, Silva FJ. Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations. Trans Am Math Soc. 2014;366:2063–2087.
- Aubin JP, Frankowska H. Set-valued analysis. Basel: Birkhäuser; 2009. (Modern Birkhäuser classics).