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Article

Pareto Optimality for Multioptimization of Continuous Linear Operators

1
Department of Electronics, College of Engineering, University of Cadiz, 11510 Puerto Real, Spain
2
Department of Mathematics, College of Engineering, University of Cadiz, 11510 Puerto Real, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Juan Luis García Guirao
Symmetry 2021, 13(4), 661; https://doi.org/10.3390/sym13040661
Received: 11 March 2021 / Revised: 29 March 2021 / Accepted: 8 April 2021 / Published: 12 April 2021
This manuscript determines the set of Pareto optimal solutions of certain multiobjective-optimization problems involving continuous linear operators defined on Banach spaces and Hilbert spaces. These multioptimization problems typically arise in engineering. In order to accomplish our goals, we first characterize, in an abstract setting, the set of Pareto optimal solutions of any multiobjective optimization problem. We then provide sufficient topological conditions to ensure the existence of Pareto optimal solutions. Next, we determine the Pareto optimal solutions of convex max–min problems involving continuous linear operators defined on Banach spaces. We prove that the set of Pareto optimal solutions of a convex max–min of form maxT(x), minx coincides with the set of multiples of supporting vectors of T. Lastly, we apply this result to convex max–min problems in the Hilbert space setting, which also applies to convex max–min problems that arise in the design of truly optimal coils in engineering. View Full-Text
Keywords: multioptimization; Pareto optimality; linear operators; adjoint operators; normed spaces; matrix norms multioptimization; Pareto optimality; linear operators; adjoint operators; normed spaces; matrix norms
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MDPI and ACS Style

Cobos-Sánchez, C.; Vilchez-Membrilla, J.A.; Campos-Jiménez, A.; García-Pacheco, F.J. Pareto Optimality for Multioptimization of Continuous Linear Operators. Symmetry 2021, 13, 661. https://doi.org/10.3390/sym13040661

AMA Style

Cobos-Sánchez C, Vilchez-Membrilla JA, Campos-Jiménez A, García-Pacheco FJ. Pareto Optimality for Multioptimization of Continuous Linear Operators. Symmetry. 2021; 13(4):661. https://doi.org/10.3390/sym13040661

Chicago/Turabian Style

Cobos-Sánchez, Clemente, José A. Vilchez-Membrilla, Almudena Campos-Jiménez, and Francisco J. García-Pacheco. 2021. "Pareto Optimality for Multioptimization of Continuous Linear Operators" Symmetry 13, no. 4: 661. https://doi.org/10.3390/sym13040661

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