On minimal extended representations of generalized power cones
| Autor: | Blanco, Víctor, Martínez-Antón, Miguel |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we analyze minimal representations of $(p,\boldsymbol{\alpha})$-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case $\boldsymbol{\alpha}$ and $p$ are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then, the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location. Comment: 23 pages, 8 figures, 4 tables |
| Databáze: | arXiv |
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