An optimization model for the management of green areas

Daniele, Patrizia; Sciacca, Daniele

doi:10.1111/itor.12987

Cited by 15 publications

(7 citation statements)

References 21 publications

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“…As established in [ 11 , 37 ], for convergence of the general iterative scheme, which induces the Euler method, the sequence must satisfy: , , , as . Conditions for convergence of this algorithm in the context of other network models as well as additional computational work can be found in [ 4 , 25 , 37 ] and in [ 8 , 31 ].…”

Section: The Algorithm and Numerical Examplesmentioning

confidence: 99%

Spatial price equilibrium networks with flow-dependent arc multipliers

Nagurney

Besik

2022

Optim Lett

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The spatial price equilibrium modeling framework, which emphasizes the importance of transportation costs between markets, has been utilized in agricultural, energy, mineral as well as financial applications. In this paper, we construct static and dynamic spatial price equilibrium networks with flow-dependent arc multipliers, which expand the reach of applications. The static model is formulated and analyzed as a variational inequality problem, whereas the dynamic one is formulated as a projected dynamical system, whose set of stationary points coincides with the set of solutions of the variational inequality. Qualitative results are presented, along with an algorithm, the Euler method, which yields a time-discretization of the continuous-time adjustment processes associated with the product shipments from supply markets to demand markets. The algorithm is implemented and applied to compute solutions to numerical examples with flow-dependent arc multipliers addressing losses and/or gains, inspired by perishable agricultural products, and by financial investments. The results in this paper add to the literature on generalized networks as well as that on commodity trade.

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Section: The Algorithm and Numerical Examplesmentioning

confidence: 99%

Spatial price equilibrium networks with flow-dependent arc multipliers

Nagurney

Besik

2022

Optim Lett

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“…Finally, we provide a sufficient condition for the strictly monotonicity of function F (see [6] for a proof).…”

Section: Variational Formulationmentioning

confidence: 99%

“…Following the well-known procedure described, for instance, in [4,6,16], we can put variational inequality (13) into standard form, that is: determine X * ∈ K such that:…”

Section: Variational Formulationmentioning

confidence: 99%

Multi-layer 5G Network Slicing with UAVs: an optimization model

Colajanni

Sciacca

2022

Preprint

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In this paper, we present a network-based optimization model describing a closed-loop supply chain for the provision of 5G network slices on demand to users and devices on the ground. The three-tier supply chain network consists of a fleet of pre-existing UAVs, to which others can be added, managed by a fleet of UAV controllers, whose purpose is to perform services requested by users and devices on the ground. The aim of this paper is to provide a constrained optimization problem through which the providers’ profits are maximized, determining the global optimal distributions of request flows, the global optimal distributions of executed services and the optimal reliability level of pre-existing UAVs of the fleet. We also derive the associated Variational inequality formulation of the problem and, finally, a numerical simulation is performed to validate the effectiveness of the model.

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“…Through KKT conditions (34) , together with conditions (35) – (42) , it is possible to derive an alternative variational formulation of the previous one provided in Section 4 (see [29] , [30] , [31] for a similar procedure). The advantage of using this new formulation lies in relaxing all the constraints present in the feasible set

within the objective function by using the associated Lagrange multipliers.…”

Section: Duality Theory and An Equivalent Formulation Of The Variatio...mentioning

confidence: 99%