# A Polynomial-Time Algorithm for Optimization of Quadratic Pseudo-Boolean Functions

We develop a polynomial-time algorithm to minimize pseudo-Boolean functions. The computational complexity is O( n^15/2), although very conservative, it is sufficient to prove that this minimization problem is in the class P. A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O( n^45/2). The algorithm was implemented in MATLAB and checked by generating one million matrices of arbitrary dimension up to 24 with random entries in the range [ -50,50]. All the experiments were successful.

READ FULL TEXT