References
- Bensoussan , A and Frehse , J . 2002 . Regularity Resuls for Nonlinear Elliptic Systems and Applications , New York : Springer Verlag .
- Gilbarg , D and Trudinger , NS . 1983 . Elliptic Partial Differential Equations of Second Order , New York : Springer Verlag .
- Maurer , H and Pickenhain , S . 1995 . Second-order sufficient conditions for control problems with mixed control-state constraints . J. Optim. Theory Appl. , 86 ( 3 ) : 649 – 667 .
- Malanowski , K . 1997 . Sufficient optimality conditions for optimal control subject to state constraints . SIAM J. Control Optim. , 35 ( 1 ) : 205 – 227 .
- Malanowski , K , Maurer , H and Pickenhain , S . 2004 . Second-order sufficient conditions for state-constrained optimal control problems . J. Optim. Theory and Appl. , 123 ( 3 ) : 595 – 617 .
- Zeidan , V . 1989 . Sufficient conditions with minimal regularity assumptions . Appl. Math. and Optim. , 20 : 19 – 31 .
- Zeidan , V . 1994 . The Riccati equation for optimal control problems with mixed state-control constraints; necessity and sufficiency . SIAM J. Control Optim. , 32 : 1297 – 1321 .
- Pickenhain , S and Tammer , K . 1991 . Sufficient conditions for local optimality in multidimensional control problems with state restrictions . Z. Anal. Anwendungen , 10 ( 3 ) : 397 – 405 .
- Pickenhain , S . 1992 . Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions . Z. Anal. Anwendungen , 11 ( 4 ) : 559 – 568 .
- Klöetzler , R . 1979 . “ On a general conception of duality in optimal control ” . In Proceedings Equadiff IV (Prague, 1977); 189–196; Lecture Notes in Math., 703 , 189 – 196 . Berlin : Springer .
- Krotov , V . 1996 . “ Global Methods in Optimal Control Theory ” . In Monographs and Textbooks in Pure and Applied Mathematics , New York : Marcel Dekker Inc, 195 .
- Casas , E , Tröltzsch , F and Unger , A . 2000 . Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations . SIAM J. Control Optim. , 38 ( 5 ) : 1369 – 1391 .
- Rösch , A and Tröltzsch , FA . 2003 . Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise control-state constraints . SIAM J. Control Optim. , 42 ( 1 ) : 138 – 154 .
- Galewska , E and Nowakowski , A . 2005 . Multidimensional dual dynamic programming . J. Optim. Theory Appl. , 124 ( 1 ) : 175 – 186 .
- Nowakowski , A . 1992 . The dual dynamic programming . Proc. Am. Math. Soc. , 116 ( 4 ) : 1089 – 1096 .
- Fleming , WH and Rishel , RW . 1975 . Deterministic and Stochastic Optimal Control , New York : Springer Verlag .
- Galewska , E and Nowakowski , A . 2006 . A dual dynamic programming for multidimensional elliptic optimal control problems . Numer. Funct. Anal. Optim. , 27 ( 3–4 ) : 279 – 289 .