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:<math>x \mapsto c x_1^{a_1} x_2^{a_2} \cdots x_n^{a_n} </math>
where <math> c > 0 \ </math> and <math>a_i \in \mathbb{R} </math>. A posynomial is any sum of monomials. <ref name="tutorial">S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi. ''[http://www.stanford.edu/~boyd/gp_tutorial.html A Tutorial on Geometric Programming].'' Retrieved 8 January 2019.</ref>
GPs have numerous applications, such as component sizing in [[Integrated circuit|IC]] design<ref>M. Hershenson, S. Boyd, and T. Lee. ''[http://www.stanford.edu/~boyd/papers/opamp.html Optimal Design of a CMOS Op-amp via Geometric Programming].'' Retrieved 8 January 2019.</ref><ref> S. Boyd, S. J. Kim, D. Patil, and M. Horowitz. ''[http://www.stanford.edu/~boyd/gp_digital_ckt.html Digital Circuit Optimization via Geometric Programming].'' Retrieved 8 January 2019.</ref> and parameter estimation via [[logistic regression]] in [[statistics]]. The [[maximum likelihood]] estimator in logistic regression is a GP.
==Convex form==
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 <math>y_i = \log(x_i)</math> and taking the log of the objective and constraint functions, the functions <math>f_i</math>, i.e., the posynomials, are transformed into log-sum-exp functions, which are convex, and the functions <math>g_i</math>, i.e., the monomials, become affine. Hence, this transformation transforms every GP into an equivalent convex program. <ref
==Software==
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