On generalized geometric programming problems with non-positive variables |
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Authors: | Jung-Fa Tsai Ming-Hua Lin Yi-Chung Hu |
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Institution: | 1. Department of Business Management, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao E. Road, Taipei 10608, Taiwan;2. Department of Information Management, Shih Chien University, No. 70, Ta-Chih Street, Taipei 10462, Taiwan;3. Department of Business Administration, Chung Yuan Christian University, Chung Li 32023, Taiwan |
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Abstract: | Generalized geometric programming (GGP) problems occur frequently in engineering design and management. Some exponential-based decomposition methods have been developed for solving global optimization of GGP problems. However, the use of logarithmic/exponential transformations restricts these methods to handle the problems with strictly positive variables. This paper proposes a technique for treating non-positive variables with integer powers in GGP problems. By means of variable transformation, the GGP problem with non-positive variables can be equivalently solved with another one having positive variables. In addition, we present some computationally efficient convexification rules for signomial terms to enhance the efficiency of the optimization approach. Numerical examples are presented to demonstrate the usefulness of the proposed method in GGP problems with non-positive variables. |
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Keywords: | Global optimization Generalized geometric programming Non-positive variables Convexification |
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