Electricity power planning problem in the medium term can be modelled as a quadratic programming problem, with an indefinite objective function. Our approach for handling with such non-convexity is through the reformulation of the objective function as a difference of two convex (DC) functions. The non-convex part is linearised and a sequence of convex problems is then solved. Each problem varies from its precedent only in the part where the linearisation of the cut is performed. The use of warm-start techniques is then a key point in order to find the solution to the new problem in few iterations.
In this talk we will present some examples where the non-convexity appears, some basic aspects of the DC programming and we will conclude with some bounds on the number of steps that are necessary for going from the old solution to the new one when we use interior-point methods.
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