# Disciplined Quasiconvex Programming

## TL;DR

This paper introduces disciplined quasiconvex programming, a framework that generalizes disciplined convex programming, enabling the specification and solving of quasiconvex optimization problems within CVXPY 1.0.

## Contribution

It presents a new composition rule for quasiconvex functions and implements a framework for disciplined quasiconvex programming in CVXPY 1.0.

## Key findings

- Generalizes classical composition rule for quasiconvex functions
- Enables solving quasiconvex programs in CVXPY 1.0
- Extends disciplined convex programming to quasiconvex problems

## Abstract

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 pointwise maximums. We refer to the class of optimization problems generated by these rules, along with a base set of quasiconvex and quasiconcave functions, as disciplined quasiconvex programs. Disciplined quasiconvex programming generalizes disciplined convex programming, the class of optimization problems targeted by most modern domain-specific languages for convex optimization. We describe an implementation of disciplined quasiconvex programming that makes it possible to specify and solve quasiconvex programs in CVXPY 1.0.