A New Separable Logarithmic Algorithm for Non-Linear Optimization

Problem statement: The idea of this study stemmed from the fact that most of the currently used optimization algorithms use a local quadratic representation of the objective function. It also arisen from the fact that the objective function may not be represented adequately by quadratic functions and the global minimizer may be obtained for objective functions. So, in this study, we generalized the field of quadratic model into the field of the non-quadratic model. Approach: A new non-quadratic model was suggested for solving unconstrained optimization problems, which modified the classical Conjugate Gradient (CG) algorithm by scaling the standard quadratic model. Results: The new algorithm was derived and evaluated theoretically and numerically for some standard well-known and effective test functions. The results, in general, indicated that the new algorithm had improvements on different well-known algorithms used in this study. Conclusion: The new proposed algorithm would be generic and easy to implement in all gradient based optimization process. Its simulation results showed that it was robust and had a potential significantly enhance the computational efficiency of iterations and function evaluations.