Why Convex Optimization Is Ubiquitous and Why Pessimism Is Widely Spread

In many practical applications, the objective function is convex. The use of convex objective functions makes optimization easier, but ubiquity of such objective function is a mystery: many practical optimization problems are not easy to solve, so it is not clear why the objective function -- whose main goal is to describe our needs -- would always describe easier-to-achieve goals. In this paper, we explain this ubiquity based on the fundamental ideas about human decision making. This explanation also helps us explain why in decision making under uncertainty, people often make pessimistic decisions, i.e.., decisions based on the worst-case scenarios