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Copula theory approach to stochastic geometric programming

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Abstract

In this research, stochastic geometric programming with joint chance constraints is investigated with elliptically distributed random parameters. The constraint’s random coefficient vectors are considered dependent, and the dependence of the random vectors is handled through copulas. Moreover, Archimedean copulas are used to derive the random rows distribution. A convex approximation optimization problem is proposed for this class of stochastic geometric programming problems using a standard variable transformation. Furthermore, a piecewise tangent approximation and sequential convex approximation are employed to obtain the lower and upper bounds for the convex optimization model, respectively. Finally, an illustrative optimization example on randomly generated data is presented to demonstrate the efficiency of the methods and algorithms.

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Acknowledgements

The first author is supported by grants from the University of Tabriz. The second author is supported by grants from the Institute for Advanced Studies in Basic Sciences (IASBS), the Ministry of Science, Research and Technology of the Islamic Republic of Iran. P.M Pardalos has been supported by the Paul and Heidi Brown Preeminent Professorship at ISE (University of Florida, USA), and a Humboldt Research Award (Germany).

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Correspondence to Rashed Khanjani-Shiraz.

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Khanjani-Shiraz, R., Khodayifar, S. & Pardalos, P.M. Copula theory approach to stochastic geometric programming. J Glob Optim 81, 435–468 (2021). https://doi.org/10.1007/s10898-021-01062-7

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