Comparison of Optimization Methods with Application to a Network Containing Malicious Agents

There are different methods of solving unconstrained optimization problems, but there have been disparities in convergence speed for most of these methods. First-order methods such as the steepest descent method are very common in solving unconstrained problems but second-order methods such as the Newton-type methods enable faster convergence especially for quadratic functions. In this paper, We compare and analyse first and second order methods in solving two unconstrained problems that differ by a multiplicative perturbation parameter to show how malicious agents in a network can cause disruption. We also explore the advantages and disadvantages of the steepest descent, Newton, and Conjugate gradient methods in terms of their convergence attributes by comparing a strictly convex function with a banana-type function.