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Geometric programs are not in general convex optimization problems, but they can be transformed to convex problems by a change of variables and a transformation of the objective and constraint functions. In particular, after performing the change of variables
34:
459:
682:. Hence, this transformation transforms every GP into an equivalent convex program. In fact, this log-log transformation can be used to convert a larger class of problems, known as
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198:{\displaystyle {\begin{array}{ll}{\mbox{minimize}}&f_{0}(x)\\{\mbox{subject to}}&f_{i}(x)\leq 1,\quad i=1,\ldots ,m\\&g_{i}(x)=1,\quad i=1,\ldots ,p,\end{array}}}
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is a Python package for cleanly defining and manipulating geometric programming models. There are a number of example GP models written with this package
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is a Python-embedded modeling language for specifying and solving convex optimization problems, including GPs, GGPs, and LLCPs.
535:: any GP can be made convex by means of a change of variables. GPs have numerous applications, including component sizing in
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939:
843:
304:
are monomials. In the context of geometric programming (unlike standard mathematics), a monomial is a function from
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is a MATLAB toolbox for specifying and solving geometric programs (GPs) and generalized geometric programs (GGPs).
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701:
is a commercial solver capable of solving geometric programs as well as other non-linear optimization problems.
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Several software packages exist to assist with formulating and solving geometric programs.
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and taking the log of the objective and constraint functions, the functions
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454:{\displaystyle x\mapsto cx_{1}^{a_{1}}x_{2}^{a_{2}}\cdots x_{n}^{a_{n}}}
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Richard J. Duffin; Elmor L. Peterson; Clarence Zener (1967).
860:"Geometric Programming for Optimal Positive Linear Systems"
707:
is an open-source solver for convex optimization problems.
812:
Optimal Design of a CMOS Op-amp via
Geometric Programming
698:
844:
Geometric programming for aircraft design optimization
828:
Digital
Circuit Optimization via Geometric Programming
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S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi.
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858:Ogura, Masaki; Kishida, Masako; Lam, James (2020).
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825:S. Boyd, S. J. Kim, D. Patil, and M. Horowitz.
651:functions, which are convex, and the functions
647:, i.e., the posynomials, are transformed into
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531:Geometric programming is closely related to
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686:(LLCP), into an equivalent convex form.
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528:. A posynomial is any sum of monomials.
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864:IEEE Transactions on Automatic Control
917:A. Agrawal, S. Diamond, and S. Boyd.
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848:AIAA Journal 52.11 (2014): 2414-2426.
521:{\displaystyle a_{i}\in \mathbb {R} }
334:{\displaystyle \mathbb {R} _{++}^{n}}
7:
809:M. Hershenson, S. Boyd, and T. Lee.
768:. John Wiley and Sons. p. 278.
796:A Tutorial on Geometric Programming
551:, and parameter tuning of positive
920:Disciplined Geometric Programming.
297:{\displaystyle g_{1},\dots ,g_{p}}
247:{\displaystyle f_{0},\dots ,f_{m}}
14:
613:{\displaystyle y_{i}=\log(x_{i})}
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111:
678:, i.e., the monomials, become
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1:
541:maximum likelihood estimation
356:{\displaystyle \mathbb {R} }
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832:Retrieved 20 October 2019.
800:Retrieved 20 October 2019.
684:log-log convex programming
923:Retrieved 8 January 2019.
841:W. Hoburg and P. Abbeel.
816:Retrieved 8 January 2019.
539:design, aircraft design,
886:10.1109/TAC.2019.2960697
486:{\displaystyle c>0\ }
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26:optimization
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649:log-sum-exp
563:Convex form
363:defined as
256:posynomials
877:1904.12976
751:References
549:statistics
77:subject to
902:140222942
894:0018-9286
740:Signomial
592:
511:∈
427:⋯
377:↦
279:…
229:…
180:…
125:…
103:≤
934:Category
734:See also
690:Software
45:minimize
24:) is an
900:
892:
772:
721:GGPLAB
705:CVXOPT
680:affine
481:
464:where
208:where
898:S2CID
872:arXiv
727:CVXPY
711:GPkit
699:MOSEK
890:ISSN
770:ISBN
715:here
543:for
493:and
475:>
258:and
254:are
882:doi
589:log
559:.
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547:in
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