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Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints

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Abstract

We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach space, and with final-state constraints, pointwise pure state constraints and a mixed pointwise control-state constraint. Basing on necessary optimality conditions obtained for an abstract multiobjective optimization framework, we establish a second-order Lagrange multiplier rule, of Fritz-John type, for local weak Pareto solutions of the problem under study. As a consequence of the main result, we also derive a multiplier rule for a multiobjective optimal control model driven by a bilinear system being affine-linear in the control, and with an objective function of continuous quadratic form.

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Acknowledgements

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

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  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, Vietnam

    Tuan Nguyen Dinh

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Nguyen Dinh, T. Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints. Appl Math Optim 84 (Suppl 2), 1521–1553 (2021). https://doi.org/10.1007/s00245-021-09803-6

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