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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.
We present a composition rule involving quasiconvex functions that generalizes the classical composition rule for convex functions. This rule complements well-known rules for the curvature of quasiconvex functions under increasing functions and point
In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP). Convex-concave programming is an organized heuristic for solving nonconv
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on alternati
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective function tha
We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization. Our condit