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

Set-Valued and Variational Analysis volume 30, pages 257–281 (2022)Cite this article

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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Authors and Affiliations

  1. Department of Mathematics and Statistics, and Institute of Applied Mathematics, University of Economics Ho Chi Minh City, 59C Nguyen Dinh Chieu, D.3, Ho Chi Minh City, Vietnam

    Tuan Nguyen Dinh

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  1. Tuan Nguyen Dinh
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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