OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS

OPTIMAL CONTROL OF PDES: papers by Frédéric Bonnans

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Parabolic equations

With P. Jaisson: Optimal control of a time-dependent state constrained parabolic equation. Rapport de Recherche INRIA RR 6784, Dec. 2008. SIAM J. Control Optim. 48-7 (2010), pp. 4550-4571.
With D. Tiba: Control problems with mixed constraints and application to an optimal investment problem. Mathematical Reports (Romanian Academy of Sciences) Vol. 11 (61), no.4 (2009), 293--306. Inria report.
With D. Tiba: Control problems with mixed constraints and application to an optimal investment problem.. Dedicated to Dr. Constantin Varsan on the occasion of his 70th Birthday. Mathematical Reports (of the Romanian Academy of Sciences) Vol. 11-4, 2009, 293-306.
With E. Casas: On the choice of the function spaces for some state-constrained control problems . Numerical Functional Analysis and Optimization 7-4 (1984), 333-348.
Analysis and control of a non-linear parabolic unstable system. J. of Large Scale Systems 6-3(1984), 249-262.

Elliptic equations

T. Bayen, J.F. Bonnans, F. Silva: Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations. Rapport de Recherche INRIA RR 7765, Oct. 2011.
J.F. Bonnans, F. Silva: Asymptotic expansions for the solution of a penalized control constrained semilinear elliptic problem. Asymptotic Expansion for the Solutions of Control Constrained Semilinear Elliptic Problems with Interior Penalties. SIAM J. Control Optim. 49, pp. 2494-2517.
With H. Zidani: Optimal control problems with partially polyhedric constraints. SIAM J. Control Optimization 37 (1999), 1726--1741. Preprint
Second order analysis for control constrained optimal control problems of semilinear elliptic systems. Applied Math. Optimization (1998), 38-3, 303-325. Preprint
With E. Casas: An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. SIAM J. Control Optimization 33-1(1995), 274-298. Pdf Preprint.
With E. Casas: A boundary Pontryagin's principle for the optimal control of state constrained elliptic systems Proc. French-Romanian Conference on Optimization, Optimal Control and Partial Differential Equations, Int. Ser. Num. Math. 107, V. Barbu, J.F. Bonnans and D. Tiba eds., Birkhauser, 241-249.
With E. Casas: Pdf Preprint. An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities. SIAM J. Control Optimization 33-1(1995), 274-298.
With E. Casas: Some stability concepts and their applications in optimal control problems. IMA Preprint 1081 (1992).
With D. Tiba: Pontryagin's principle in the control of semilinear elliptic variational inequalities. Applied Mathematics and Optimization 23-3(1991), 299-312.
Pontryagin's principle for the optimal control of semilinear elliptic systems with state constraints. 30th IEEE Conference on Decision and Control, Vol. 2(1991), 1976-1979, Brighton, England.
With E. Casas: Optimal Control of Semilinear Multistate Systems with State Constraints. SIAM J. Control Optimization 27-2 (1989), 446-455.
With E. Casas: Controle de systemes elliptiques semilinéaires comportant des contraintes sur l'état . In "Nonlinear partial differential equations and their applications, Collège de France seminar vol. VIII", H. Brézis and J.L. Lions eds., Pitman Research Notes in Mathematics Series 166, Longman Scientific and Technical, New York, 1988, p. 69-86.