Geometric programming is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Conventional geometric programming models assume deterministic and precise parameters. However, the values observed for the parameters in real-world geometric programming problems often are imprecise and vague. We use geometric programming within an uncertainty-based framework proposing a chance-constrained geometric programming model whose coefficients are uncertain variables. We assume the uncertain variables to have normal, linear and zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained geometric programming problems can be transformed into conventional geometric programming problems to calculate the objective values. The efficacy of the procedures and algorithms is demonstrated through numerical examples.

Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions / Khanjani Shiraz, R.; Tavana, M.; Di Caprio, D.; Fukuyama, H.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 1573-2878. - 170:1(2016), pp. 243-265. [10.1007/s10957-015-0857-y]

### Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions

#### Abstract

Geometric programming is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Conventional geometric programming models assume deterministic and precise parameters. However, the values observed for the parameters in real-world geometric programming problems often are imprecise and vague. We use geometric programming within an uncertainty-based framework proposing a chance-constrained geometric programming model whose coefficients are uncertain variables. We assume the uncertain variables to have normal, linear and zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained geometric programming problems can be transformed into conventional geometric programming problems to calculate the objective values. The efficacy of the procedures and algorithms is demonstrated through numerical examples.
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2016
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Khanjani Shiraz, R.; Tavana, M.; Di Caprio, D.; Fukuyama, H.
Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions / Khanjani Shiraz, R.; Tavana, M.; Di Caprio, D.; Fukuyama, H.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 1573-2878. - 170:1(2016), pp. 243-265. [10.1007/s10957-015-0857-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11572/250256`
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