References
- Kang W , Wilcox LC . Mitigating the curse of dimensionality: sparse grids characteristics method for optimal feedback control and HJB equation. preprint, 2016.
- Bergounioux M , Merabet N . Sensitivity analysis for optimal control of problems governed by semilinear parabolic equations. Control Cybernet. 2000;29(4):861–886.
- Cannarsa P , Frankowska H , Scarinci T . Second-order sensitivity relations and regularity of the value function for Mayer’s problem in optimal control. SIAM J Control Optim. 2015;53(6):3642–3672.
- Bonnans JF , Cominetti R . Perturbed optimization in Banach spaces. I. A general theory based on a weak directional constraint qualification. SIAM J Control Optim. 1996;34(4):1151–1171.
- Bonnans JF , Cominetti R . Perturbed optimization in Banach spaces. II. A theory based on a strong directional constraint qualification. SIAM J Control Optim. 1996;34(4):1172–1189.
- Bonnans JF , Jaisson P . Optimal control of a parabolic equation with time-dependent state constraints. SIAM J Control Optim. 2010;48(7):4450–4571.
- Ito K , Kunisch K . Augmented Lagrangian-SQP methods for nonlinear optimal control problems of tracking type. SIAM J Control Optim. 1996;34(3):874–891.
- Porretta A , Zuazua E . Remarks on long time versus steady state optimal control. Cham: Springer International Publishing; 2016. p. 67–89.
- Fiacco AV . Sensitivity analysis for nonlinear programming using penalty methods. Math Program. 1976;10(3):287–311.
- Malanowski K . Stability analysis for nonlinear optimal control problems subject to state constraints. SIAM J Optim. 2007;18(3):926–945.
- Malanowski K . Stability and sensitivity analysis for linear-quadratic optimal control subject to state constraints. Optimization. 2007;56(4):463–478.
- Maurer H , Pesch HJ . Solution differentiability for nonlinear parametric control problems. SIAM J Control Optim. 1994;32(6):1542–1554.
- Sokołowski J . Sensitivity analysis of control constrained optimal control problems for distributed parameter systems. SIAM J Control Optim. 1987;25(6):1542–1556.
- Lions PL . Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. I. The case of bounded stochastic evolutions. Acta Math. 1988;161(3–4):243–278.
- Cannarsa P . Regularity properties of solutions to Hamilton-Jacobi equations in infinite dimensions and nonlinear optimal control. Differ Integral Equ. 1989;2(4):479–493.
- Cannarsa P , Frankowska H . Value function and optimality condition for semilinear control problems II. Parabolic case. Appl Math Optim. 1996;33(1):1–33.
- Cannarsa P , Frankowska H . Value function and optimality conditions for semilinear control problems. Appl Math Optim. 1992;26(2):139–169.
- Malanowski K , Tröltzsch F . Lipschitz stability of solutions to parametric optimal control problems for parabolic equations. Z Anal Anwendungen. 1999;18(2):469–489.
- Casas E . Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. SIAM J Control Optim. 1997;35(4):1297–1327.
- Raymond JP , Zidani H . Hamiltonian Pontryagin’s principles for control problems governed by semilinear parabolic equations. Appl Math Optim. 1999;39(2):143–177.
- Lions JL . Optimal control of systems governed by partial differential equations. Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170. New York (NY): Springer-Verlag; 1971.
- Tröltzsch F . Optimal control of partial differential equations. Vol. 112, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2010.
- Casas E , Kruse F , Kunisch K . Optimal control of semilinear parabolic equations by BV-functions. SIAM J Control Optim. 2017;55(3):1752–1788.
- Casas E , Tröltzsch F . Second order analysis for optimal control problems: improving results expected from abstract theory. SIAM J Optim. 2012;22(1):261–279.
- Casas E , Tröltzsch F . Second order optimality conditions and their role in PDE control. Jahresber Dtsch Math-Ver. 2015;117(1):3–44.
- Ito K , Kunisch K . Lagrange multiplier approach to variational problems and applications. Vol. 15, Advances in design and control. Philadelphia (PA): Society for Industrial and Applied Mathematics (SIAM); 2008.
- Hinze M , Pinnau R , Ulbrich M , Ulbrich S . Optimization with PDE constraints. Vol. 23, Mathematical modelling: theory and applications. New York (NY): Springer; 2009.