Penalty Algorithm Based on Three-Term Conjugate Gradient Method for Unconstrained Optimization Portfolio Management Problems

In a class of solving unconstrained optimization problems, the conjugate gradient method has been proved to be efficient by researchers' due to it's smaller storage requirements and computational cost. Then, a class of penalty algorithms based on three-term conjugate gradient methods was developed and extend to and solution of an unconstrained minimization portfolio management problems, where the objective function is a piecewise quadratic polynomial. By implementing the proposed algorithm to solve some selected unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time. It was shown that this algorithm is promising.