A Fourth-Order Nonlinear Conjugate Gradient Method in Equality Constrained Optimization

This paper presents a fourth-order nonlinear conjugate gradient method in equality constrained optimization. The idea is to transform the constrained problem into unconstrained type through the Lagrange multipliers scheme. Using four terms of Taylor series development, we approximate the transformed function (augmented Lagrange function). Lastly, we employ the new fourth-order nonlinear conjugate gradient method in equality constrained optimization to solve the optimization problem. We present the algorithm in steps and some properties of the gradients are proved, using classical results. Also, the convergence analysis has been proved under classical and known assumptions. Furthermore, we present the obtained numerical results and compare them to some existing results. The analysis of results confirms that the new method is accurate.