Pareto Optimality for Multioptimization of Continuous Linear Operators

Sánchez, Clemente Cobos; Membrilla, Jose Antonio Vilchez; Campos-Jiménez, Almudena; García-Pacheco, Francisco Javier

doi:10.3390/sym13040661

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…We refer the reader to [2,21,22] for a topological and geometrical study of the set of supporting vectors of a continuous linear operator. Supporting vectors have been successfully applied to solve multiobjective optimization problems that typically arise in Bioengineering, Physics, and Statistics [14,15,[23][24][25], improving considerably the results obtained by means of other techniques, such as Heuristic methods [16,18,19]. Definition 2 (1-Supporting vector).…”

Section: Supporting Vectorsmentioning

confidence: 99%

Analytical Solutions to Minimum-Norm Problems

et al. 2022

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For G∈Rm×n and g∈Rm, the minimization min∥Gψ−g∥2, with ψ∈Rn, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is min∥T(h)−k∥, where T:H→K is a continuous linear operator between Hilbert spaces H,K and h∈H,k∈K. In order to avoid an unbounded set of solutions for the Tykhonov regularization, we transform the infinite-dimensional Tykhonov regularization into a multiobjective optimization problem: min∥T(h)−k∥andmin∥h∥. We call it bounded Tykhonov regularization. A Pareto-optimal solution of the bounded Tykhonov regularization is found. Finally, the bounded Tykhonov regularization is modified to introduce the precise Tykhonov regularization: min∥T(h)−k∥with∥h∥=α. The precise Tykhonov regularization is also optimally solved. All of these mathematical solutions are optimal for the design of Magnetic Resonance Imaging (MRI) coils.

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Section: Supporting Vectorsmentioning

confidence: 99%

Analytical Solutions to Minimum-Norm Problems

et al. 2022

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“…The saddle point optimality conditions are briefly explained in [13], Rooyen et al [14] constructed a Langrangian function for the convex multiobjective problem and established a relationship between saddle point optimality conditions and Pareto optimal solutions. Cobos-Sànchez et al [15] proposed Pareto optimality conditions for multiobjective optimization problems of continuous linear operators. Recently, Treanta [16] studied robust saddle point criterion in second order partial differential equations and partial differential inequations.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Convex Optimization in Real Banach Space

Lai

Hassan

Maurya³

et al. 2021

Symmetry

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In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

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Energy Coherent Fog Networks Using Multi-Sink Wireless Sensor Networks

et al. 2021

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Fog computing (FC) models the cloud computing paradigm expedient by bridging the breach between centralized data servers and diverse terrestrially distributed applications. It wields various wireless sensor networks (WSNs) that sprawl in the core of any IoT applications. Consequently, the operation of fog network turns on the efficiency of WSNs operation, while the all-inclusive network energy consumption depends on both FC and WSNs operation. This paper addresses how dissimilar organizations of a fog network can influence its effectiveness and energy savings. Chiefly, it appraises whether deploying multisink nodes in close enough vicinity to the fog nodes can give in energy savings and foster coherent data communication between WSNs and fog networks. To assess the multi-sink assignment problem the following four criteria are used: (i) Distance from the fog network nodes; (ii) Nodes degree; (iii) Sink nodes energy; and (iv) Sink nodes processing capabilities. This paper suggests four novel solutions to the multisink connectivity for some challenges of fog networks deeming: (i) Window Nondominant Set (WNS); (ii) Evaluation Based Approach (EBA); (iii) Harris Hawks Optimizer (HHO); and (iv) Modified HHO (MHHO). Distinct sets of experiments are conducted to check out algorithmic performance. The performance of all algorithms is measured and then compared to each other in terms of power consumption, runtime, packet loss, and localization error. One of the key supremacies of our approaches is the utilization of fog network for sensor networks data processing, principally with the large-scale networks. Yet, the communication challenges could need further study due to the limited communication range of the sensors.

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Pareto Optimality for Multioptimization of Continuous Linear Operators

Cited by 6 publications

References 28 publications

Analytical Solutions to Minimum-Norm Problems

Analytical Solutions to Minimum-Norm Problems

Multiobjective Convex Optimization in Real Banach Space

Energy Coherent Fog Networks Using Multi-Sink Wireless Sensor Networks

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