Disciplined Geometric Programming

TL;DR

This paper introduces log-log convex programming, a generalization of geometric programming, with a disciplined framework and implementation in CVXPY for solving a broader class of convex optimization problems.

Contribution

It defines log-log convex functions, develops disciplined geometric programming, and implements it in CVXPY, expanding the scope of convex optimization techniques.

Findings

Log-log convex functions include well-known and new functions.

Disciplined geometric programming enables systematic problem formulation.

Implementation in CVXPY facilitates practical problem solving.

Abstract

We introduce log-log convex programs, which are optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs, which we refer to as a log-log transformation. This class of problems generalizes traditional geometric programming and generalized geometric programming, and it includes interesting problems involving nonnegative matrices. We give examples of log-log convex functions, some well-known and some less so, and we develop an analog of disciplined convex programming, which we call disciplined geometric programming. Disciplined geometric programming is a subclass of log-log convex programming generated by a composition rule and a set of functions with known curvature under the log-log transformation. Finally, we describe an implementation of disciplined geometric programming as a reduction in CVXPY 1.0.