The algorithm presented here combines Boolean logic analysis with heuristic search to solve the general 0-1 polynomial programming problem. It can also be extended to solve continuous variable problems, after the problem has been converted to discrete polynomial form. Logic relations embedded in 0-1 variables are explored by a simple consensus operation to serve as the main minimization strategy. The procedure for sequential generation of prime implicants avoids rapidly increasing the number of prime implicants when problems become large. The computational results indicate that this algorithm is quite reliable for 0-1 problem formulations.