A Tutorial on the CVX System for Modeling and Solving Convex Optimization Problems

Abstract

In many areas of knowledge, situations in which we have to model and solve optimization problems are recurrent. Among the mathematical theories that support the solution of such problems, convex optimization unveiled to be an important tool. This is mainly due to the existence of algorithms whose computational solution has matured a lot in terms of speed of solution and reliability during the past few years. In this context, it deserves attention the CVX, a system for modeling and solving convex optimization problems. CVX uses the disciplined convex programming concept, which is a set of conventions or rules that permits the verification of convexity and automatic conversion of the problem instance into forms directly handled by the embedded solvers. This tutorial presents CVX in a didactic manner whose objective is to facilitate the learning about using the tool along with disciplined convex programming. Besides a number of examples, the tutorial also provides some applications, their corresponding CVX codes, the numerical solutions and discussions.