Convex Optimization

Convex optimization refers to problems whose geometry is well-behaved. If a problem is convex, any local minimum is also a global minimum, which makes optimization far more reliable. This property is extremely valuable theoretically because it simplifies the question, “Is the solution I found actually the best one?” Logistic regression, some forms of SVM, and several statistical estimation problems belong to this class. In optimization, convexity is almost like working on safe terrain.