An orthogonal projection algorithm for solving quadratic programming problems

Abstract

In this paper, we combine the classical method of unconstrained optimization, the methods for solving linear programming problems and the orthogonal projection technique to evolve a new algorithm for solving quadratic programming problems. We solve the quadratic programming problem ignoring the constraints using the classical method to obtain the unconstrained optimum. The unconstrained optimum is then tested for feasibility in the original quadratic programming problem. Feasibility of the unconstrained optimum implies that it is optimal solution to the original problem. If the unconstrained optimum is infeasible we then make moves to search for the feasible optimal solution by projecting it orthogonally on the hyper-plane of each of the violated constraints. Feasibility of any of the projected points indicates optimal solution, while infeasibility indicates that the optimal solution is at extreme point of the feasible region and is obtained by solving linear approximation of the quadratic programming problem. From the computational results, our proposed algorithm performed well to solve quadratic programming problems.