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Geometric Programming: Methods, Computations and Applications
Abstract
In this paper, we give an applications-oriented survey of geometric programming. This important class of nonlinear programming problems has been intensively studied over the past decade and has played a crucial role in an extremely broad range of applications. The focus of the paper will be on posynomial programs and the slightly more general class of signomial programs. The approach used in studying posynomial programs has been generalized to a much broader class of optimization problems, and an excellent survey of that generalized theory recently appeared in a paper by E. L. Peterson [SIAM Rev., 18 (1976), pp. 1–51]. We do not consider that generalized theory here. It is our intent to provide the reader with an understanding of the basic results in posynomial and signomial programming that have played a crucial role in applications. After reviewing these basic results, we consider computational methods and applications. Three specific applications are considered in detail, and a bibliography indicating the broad range of applications is given.
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Cited by
A tutorial on geometric programming
Boyd, S., Kim, S.-J., Vandenberghe, L., & Hassibi, A. (2007) · Optimization and Engineering · doi:10.1007/s11081-007-9001-7 · Cited by 1,195
Disciplined Convex Programming
Grant, M., Boyd, S., & Ye, Y. (2006) · Nonconvex Optimization and Its Applications · doi:10.1007/0-387-30528-9_7 · Cited by 1,026
Optimal estimation theory for dynamic systems with set membership uncertainty
Milanese, M., & Vicino, A. (1991) · Automatica · doi:10.1016/0005-1098(91)90134-n · Cited by 683
Optimal design of a CMOS op-amp via geometric programming
Hershenson, M. D., Boyd, S. P., & Lee, T. H. (2001) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/43.905671 · Cited by 548
Performance optimization of VLSI interconnect layout
Cong, J., He, L., Koh, C.-K., & Madden, P. H. (1996) · Integration · doi:10.1016/s0167-9260(96)00008-9 · Cited by 334
Metadata
- Authors
- Ecker, J. G.
- Venue
- SIAM Review
- Published
- 1980-07
- Volume
- 22
- Issue
- 3
- Pages
- 338-362
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W1992651809
- Cited by
- 189
- References
- 0
- FWCI
- 0.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ecker, J. G. (1980). Geometric Programming: Methods, Computations and Applications. SIAM Review. https://doi.org/10.1137/1022058
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