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Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Semilinear Parabolic Equations

Abstract

We consider multiobjective optimal control problems for semilinear parabolic systems subject to pointwise state constraints, integral state-control constraints and pointwise state-control constraints. In addition, the data of the problems need not be twice Fréchet differentiable. Employing the second-order directional derivative (in the sense of Demyanov-Pevnyi) for the involved functions, we establish necessary optimality conditions, via second-order Lagrange multiplier rules of Fritz-John type, for local weak Pareto solutions of the problems.

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Acknowledgments

The author would like to thank the editor and the referees for their valuable remarks and suggestions, which have helped him to greatly improve the paper.

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Correspondence to Tuan Nguyen Dinh.

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This work was supported by a Grant of the UEH Foundation for Academic Research.

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Dinh, T.N. Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Semilinear Parabolic Equations. Set-Valued Var. Anal 30, 257–281 (2022). https://doi.org/10.1007/s11228-020-00555-z

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  • DOI: https://doi.org/10.1007/s11228-020-00555-z

Keywords

  • Multiobjective optimal control
  • Semilinear parabolic equation
  • Necessary second-order optimality condition
  • Local weak Pareto solution
  • Second-order directional derivative

Mathematics Subject Classification (2010)

  • 35J25
  • 49K20
  • 49K27
  • 90C29
  • 90C46