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Nathalie Khalil

Publications and source records attributed to Nathalie Khalil.

3 recordsLinked to original sources

Bilevel optimization for smart irrigation control: a framework for enhancing water-use efficiency in agriculture

Global warming has intensified water scarcity, posing a critical challenge for the agricultural sector, where seasonal demand often leads to significant wastage. This work addresses the need for efficient water management by proposing a smart irrigation control system based on a bilevel optimization algorithm. The framework aims to minimize water consumption across multiple fields simultaneously or, under supply constraints, to distribute available water equitably to minimize deviations from required levels. To achieve this, the problem is modeled hierarchically: the upper level acts as a central controller managing daily water limits and field-wise allocation, while the lower level acts as a centralized scheduler determining the optimal cooperative irrigation execution across all fields. This structure ensures that both global resource constraints and local irrigation needs are met efficiently. Preliminary results from digital simulation tools suggest that the proposed framework significantly improves water-use efficiency and supports sustainable irrigation practices, particularly in water-constrained scenarios.

math.OC

Necessary Optimality Conditions For Average Cost Minimization Problems

Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this paper, we provide necessary optimality conditions for a nonrestrictive class of optimal control problems in which unknown parameters intervene in the dynamics, the cost function and the right end-point constraint. An important feature of our results is that we allow the unknown parameters belonging to a mere complete separable metric space (not necessarily compact).

math.OC

Normality of Necessary Optimality Conditions for Calculus of Variations Problems with State Constraints

We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint qualification that we suggest here), then the necessary optimality conditions apply in the normal form. We establish normality results for (weak) local minimizers and global minimizers, employing two different approaches and invoking slightly diverse assumptions. More precisely, for the local minimizers result, the Lagrangian is supposed to be Lipschitz with respect to the state variable, and just lower semicontinuous in its third variable. On the other hand, the approach for the global minimizers result (which is simpler) requires the Lagrangian to be convex with respect to its third variable, but the Lipschitz constant of the Lagrangian with respect to the state variable might now depend on time.

math.OC