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References (23)
-
D. Gilbarg, N. Trudinger (1977)
Elliptic Partial Differential Equa-tions of Second Order -
S. Robinson (1980)
Strongly Regular Generalized EquationsMath. Oper. Res., 5
-
Perturbation analysis of optimization problems, in preparation -
K. Malanowski (1992)
Second-order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spacesApplied Mathematics and Optimization, 25
-
E. Casas, F. Tröltzsch, A. Unger (1996)
Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control ProblemZeitschrift Fur Analysis Und Ihre Anwendungen, 15
-
J. Bonnans, A. Shapiro, J. Bonnans (1998)
Optimization Problems with Perturbations: A Guided TourSIAM Rev., 40
-
K. Malanowski (1995)
Stability and sensitivity of solutions to nonlinear optimal control problemsApplied Mathematics and Optimization, 32
-
R. Cominetti (1990)
Metric regularity, tangent sets, and second-order optimality conditionsApplied Mathematics and Optimization, 21
-
J. Sokołowski (1987)
Sensitivity analysis of control constrained optimal control problems for distributed parameter systemsSiam Journal on Control and Optimization, 25
-
H. Maurer, J. Zowe (1979)
First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problemsMathematical Programming, 16
-
The tangent optimization problem -
A. Ioffe, V. Tikhomirov (1979)
Theory of extremal problems -
J. Bonnans, R. Cominetti (1996)
Perturbed Optimization in Banach spaces I: A General Theory based on a Weak Directional Constraint QualificationSiam Journal on Control and Optimization, 34
-
(1972)
Probl emes unilat eraux -
(1976)
Contr^ ole dans les in equations variationnelles elliptiques -
E. Casas, F. Tröltzsch, A. Unger (2000)
Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic EquationsSIAM J. Control. Optim., 38
-
F. Bonnans, E. Casas (1995)
An Extension of Pontryagin's Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational InequalitiesSiam Journal on Control and Optimization, 33
-
A. Haraux (1977)
How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalitiesJournal of The Mathematical Society of Japan, 29
-
S. Agmon, A. Douglis, L. Nirenberg (1959)
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. ICommunications on Pure and Applied Mathematics, 12
-
R. Rockafellar (1987)
Conjugate Duality and Optimization -
E. Casas, F. Tröltzsch (1999)
Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic EquationsApplied Mathematics and Optimization, 39
-
H. Maurer, J. Zowe (1979)
Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problemsMathematical Programming, 16
-
(1968)
Contr^ ole optimal de syst emes gouvern es par des equations aux d eriv ees partielles INRIA Second order analysis for control constrained optimal control problems 23
- Publisher
- Springer Journals
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s002459900093
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. This paper presents a second-order analysis for a simple model optimal control problem of a partial differential equation, namely, a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be minimized is a standard quadratic functional. Assuming the feasible set to be polyhedric, we state necessary and sufficient second-order optimality conditions, including a characterization of the quadratic growth condition. Assuming that the second-order sufficient condition holds, we give a formula for the second-order expansion of the value of the problem as well as the directional derivative of the optimal control, when the cost function is perturbed. Then we extend the theory of second-order optimality conditions to the case of vector-valued controls when the feasible set is defined by local and smooth convex constraints. When the space dimension n is greater than 3, the results are based on a two norms approach, involving spaces L 2 \((\Omega)\) and L s \((\Omega)\) , with s>n/2 .
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Dec 1, 1998
Keywords: Key words. Optimal control, Elliptic systems, Sensitivity analysis, Expansion of solutions, Second-order optimality conditions, Legendre forms, Polyhedricity, Two norms approach. AMS Classification. Primary 49K40, Secondary 49K20, 35B30, 35J60, 90C31.