Regular lagrange multipliers for control problems with mixed pointwise control-state constraints

SIAM Journal on Optimization

Volumn 15, Issue 2, 2005, Pages 616-634

  Tröltzsch, Fredi ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Elliptic and parabolic equations; Hubert space; Mixed pointwise control state constraint; Optimal control; Quadratic programming; Regular Lagrange multipliers

Indexed keywords

CONSTRAINT THEORY; CONTROL; FUNCTIONS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; QUADRATIC PROGRAMMING; SET THEORY;

ELLIPTIC AND PARABOLIC EQUATIONS; HILBERT SPACE; MIXED POINTWISE CONTROL-STATE CONSTRAINT; OPTIMAL CONTROL; REGULAR LAGRANGE MULTIPLIERS;

LAGRANGE MULTIPLIERS;

EID: 18844446483     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623403426519     Document Type: Article

References (15)

1. N. ARADA AND J. P. RAYMOND, Optimal control problems with mixed control-state constraints, SIAM J. Control Optim., 39 (2000), pp. 1391-1407.
2. M. BERGOUNIOUX AND F. TRÖLTZSCH, Optimal control of linear bottleneck problems, ESAIM Control Optim. Calc. Var., 3 (1998), pp. 235-250.
3. M. BERGOUNIOUX AND F. TRÖLTZSCH, Optimal control of semilinear parabolic equations with state-constraints of bottleneck type, ESAIM Control Optim. Calc. Var., 4 (1999), pp. 595-608.
4. E. CASAS, J.-P. RAYMOND, AND H. ZIDANI, Pontryagin's principle for local solutions of control problems with mixed control-state constraints, SIAM J. Control Optim., 39 (2000), pp. 1182-1203.
5. E. CASAS, F. TRÖLTZSCH, AND A. UNGER, Second order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations, SIAM J. Control Optim., 38 (2000), pp. 1369-1391.
6. I. EKELAND AND R. TEMAM, Analyse Convexe et Problèmes Variationnels, Dunod, Gauthier-Villars, Paris, 1974.
7. N. LEVINSON, A class of continuous linear programming problems, J. Math. Anal. Appl., 16 (1966), pp. 73-83.
8. D. G. LUENBERGER, Optimization by Vector Space Methods, Wiley, New York, 1969.
9. J.-P. RAYMOND AND F. TRÖLTZSCH, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints, Discrete Contin. Dynam. Systems, 6 (2000), pp. 431-450.
10. R. T. ROCKAFELLAR, Extension of Fenchel's duality theorem for convex functions, Duke Math. J., 33 (1966), pp. 81-90.
11. R. T. ROCKAFELLAR, Duality and stability in extremum problems involving convex functions, Pacific J. Math., 21 (1967), pp. 167-187.
12. R. T. ROCKAFELLAR, Convex functions and duality in optimization problems and dynamics, in Mathematical Systems Theory and Economics, Vol. II, Lect. Notes in Oper. Res. and Math. Econ. 12, Springer, Berlin, 1969, pp. 117-141.
13. A. RÖSCH AND F. TRÖLTZSCH, Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise control-state constraints, SIAM J. Control Optim., 42 (2003), pp. 138-154.
14. F. TRÖLTZSCH, A minimum principle and a generalized bang-bang principle for a distributed optimal control problem with constraints on the control and the state, ZAMM Z. Angew. Math. Mech., 59 (1979), pp. 737-739.
15. W. F. TYNDALL, A duality theorem for a class of continuous linear programming problems, J. SIAM, 13 (1965), pp. 644-666.