Geometric programming: Difference between revisions

Revision as of 21:07, 10 January 2019

Revision as of 21:08, 10 January 2019

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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 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 name="tutorial"/> In fact, this log-log transformation can be used to convert a larger class of problems, known as log-log convex programs (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==

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* [https://github.com/convexengineering/gpkit GPkit] is a Python package for cleanly defining and manipulating geometric programming models. There are a number of example GP models written with this package [https://github.com/convexengineering/gplibrary here].

*[https://web.stanford.edu/~boyd/ggplab/ GGPLAB] is a MATLAB toolbox for specifying and solving geometric programs (GPs) and generalized geometric programs (GGPs).

* [https://www.cvxpy.org/tutorial/dgp/index.html CVXPY] is a Python-embedded modeling language for specifying and solving convex optimization problems, including GPs, GGPs, and log-log convex programsLLCPs. <ref name="dgp"/>

==See also==