Engineering and Business Applications of Sum of Squares Polynomials

Understand

Optimizing over the cone of nonnegative polynomials, and its dual counterpart, optimizing over the space of moments that admit a representing measure, are fundamental problems that appear in many different applications from engineering and computational mathematics to business.

• In this paper, we review a number of these applications.
• These include, but are not limited to, problems in control (e.g., formal safety verification), finance (e.g., option pricing), statistics and machine learning (e.g., shape-constrained regression and optimal design), and game theory (e.g., Nash equilibria computation in polynomial games).
• We then show how sum of squares techniques can be used to tackle these problems, which are hard to solve in general.