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July  2014, 10(3): 761-776. doi: 10.3934/jimo.2014.10.761

## A hydrothermal problem with non-smooth Lagrangian

 1 University of Oviedo, Department of Mathematics, E.P.I, Campus of Viesques, Gijón, 33203, Spain, Spain, Spain, Spain

Received  September 2012 Revised  June 2013 Published  November 2013

This paper deals with the optimization of a hydrothermal problem that considers a non-smooth Lagrangian $L(t ,z,z^{\prime})$. We consider a general case where the functions $L_{z^{\prime}}(t ,\cdot,\cdot)$ and $L_{z}(t ,\cdot ,\cdot)$ are discontinuous in $\{(t,z,z^{\prime})/z^{\prime}=\phi(t,z)\}$, which is the borderline point between two power generation zones. This situation arises in problems of optimization of hydrothermal systems where the thermal plant input-output curve considers the shape of the cost curve in the neighborhood of the valve points. The problem shall be formulated in the framework of nonsmooth analysis, using the generalized (or Clarke's) gradient. We shall obtain a necessary minimum condition and we shall generalize the known result (smooth transition) that the derivative of the minimum presents a constancy interval. Finally, we shall present an example.
Citation: Luis Bayón, Jose Maria Grau, Maria del Mar Ruiz, Pedro Maria Suárez. A hydrothermal problem with non-smooth Lagrangian. Journal of Industrial & Management Optimization, 2014, 10 (3) : 761-776. doi: 10.3934/jimo.2014.10.761
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