Geometric programming: Difference between revisions

Revision as of 03:23, 19 January 2020

Revision as of 13:46, 23 March 2020

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==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 [[LogSumExp | log-sum-exp]] functions, which are convex, and the functions <math>g_i</math>, i.e., the monomials, become [[affine transformation | affine]]. Hence, this transformation transforms every GP into an equivalent convex program. <ref name="tutorial"/> In fact, this log-log transformation can be used to convert a larger class of problems, known as [[log-log convex programming]] (LLCP), into an equivalent convex form. <ref name="dgp">A. Agrawal, S. Diamond, and S. Boyd. ''[https://arxiv.org/abs/1812.04074 Disciplined Geometric Programming.]'' Retrieved 8 January 2019.</ref>

==Software==