What is the meaning of SOS basis?

SOS basis, or Sum of Squares basis, refers to a mathematical representation used in optimization, particularly in the context of polynomial equations. It involves expressing a polynomial as a sum of squares of other polynomials, which is important for ensuring non-negativity in optimization problems. This concept is often applied in fields like control theory, algebraic geometry, and real algebraic geometry, where it aids in determining feasible solutions within certain constraints.