Copula theory approach to stochastic geometric programming

Rashed Khanjani-Shiraz (), Salman Khodayifar () and Panos M. Pardalos ()
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Rashed Khanjani-Shiraz: University of Tabriz
Salman Khodayifar: Institute for Advanced Studies in Basic Sciences (IASBS)
Panos M. Pardalos: University of Florida

Journal of Global Optimization, 2021, vol. 81, issue 2, No 7, 435-468

Abstract: 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.

Keywords: Geometric programming; Joint chance-constraint programming; Copula theory; Archimedean Copulas (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-021-01062-7

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