This book deals with the construction of an orthogonal projection algorithm for solutions of quadratic programming problems. The algorithm starts by finding the unconstrained optimum using the classical theory of differentiation and then tests the solution for feasibility in the constrained problem. If the unconstrained optimum is infeasible in the constrained problem, then the algorithm makes a move to search for the optimum solution which in most situations is achievable in only one step. The work-ability of the algorithm is shown by applying it in solving several quadratic programming problems. The solutions obtained by using the Projection Algorithm are compared with those obtained by using OPTIMIZER software. The projection algorithm is found to give the same or better optimal solutions than the OPTIMIZER.