Based on recent work by Powell, a new optimization algorithm is presented. It merges the Newton-Raphson method and quadratic programming. A unique feature is that one does not converge the equality and tight inequality constraints for each step taken by the optimization algorithm. The article show how to perform the necessary calculations efficiently for very large problems which require the use of mass memory. Experience with the algorithm on small problems indicates it converges exceptionally quickly to the optimal answer, often in as few iterations (5 to 15) as are needed to perform a single simulation with no optimization using more conventional approaches.