TY - JOUR
T1 - A Riemannian subgradient algorithm for economic dispatch with valve-point effect
AU - Borckmans, Pierre B.
AU - Easter Selvan, S.
AU - Boumal, Nicolas
AU - Absil, P. A.
N1 - Funding Information:
The first author was supported by a FRIA (Fonds pour la formation à la Recherche dans l’Industrie et dans l’Agriculture) fellowship. The third author was supported by a FNRS (Fonds National de la Recherche Scientifique) fellowship.
Funding Information:
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization) , funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office. This work was financially supported by the Belgian FRFC (Fonds de la Recherche Fondamentale Collective) .
PY - 2014
Y1 - 2014
N2 - The economic load dispatch problem (ELDP) is a classical problem in the power systems community. It consists in the optimal scheduling of the output of power generating units to meet the required load demand subject to unit and system inequality and equality constraints. This optimization problem is challenging on three different levels: the geometry of its feasible set, the non-differentiability of its cost function and the multimodal aspect of its landscape. For this reason, ELDP has received much attention in the past few years and numerous derivative-free techniques have been proposed to tackle its multimodal and nondifferentiable characteristics. In this work we propose a different approach, exploiting the rich geometrical structure of the problem. We show that the (nonlinear) equality constraint can be handled in the framework of Riemannian manifolds and we develop a feasible (all iterates satisfy the constraints) subgradient descent algorithm to provide fast convergence to local minima. To this end, we show that Clarke's calculus can be used to compute a deterministic admissible descent direction by solving a simple, low-dimensional quadratic program. We test our approach on four real data sets. The proposed method provides fast local convergence and scales well with respect to the problem dimension. Finally, we show that the proposed algorithm, being a local optimization method, can be incorporated in existing heuristic techniques to provide a better exploration of the search space.
AB - The economic load dispatch problem (ELDP) is a classical problem in the power systems community. It consists in the optimal scheduling of the output of power generating units to meet the required load demand subject to unit and system inequality and equality constraints. This optimization problem is challenging on three different levels: the geometry of its feasible set, the non-differentiability of its cost function and the multimodal aspect of its landscape. For this reason, ELDP has received much attention in the past few years and numerous derivative-free techniques have been proposed to tackle its multimodal and nondifferentiable characteristics. In this work we propose a different approach, exploiting the rich geometrical structure of the problem. We show that the (nonlinear) equality constraint can be handled in the framework of Riemannian manifolds and we develop a feasible (all iterates satisfy the constraints) subgradient descent algorithm to provide fast convergence to local minima. To this end, we show that Clarke's calculus can be used to compute a deterministic admissible descent direction by solving a simple, low-dimensional quadratic program. We test our approach on four real data sets. The proposed method provides fast local convergence and scales well with respect to the problem dimension. Finally, we show that the proposed algorithm, being a local optimization method, can be incorporated in existing heuristic techniques to provide a better exploration of the search space.
KW - Differential geometry
KW - Economic load dispatch
KW - Nonsmooth optimization
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U2 - 10.1016/j.cam.2013.07.002
DO - 10.1016/j.cam.2013.07.002
M3 - Article
AN - SCOPUS:84881281680
SN - 0377-0427
VL - 255
SP - 848
EP - 866
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -