SOME COMPUTING RESULTS FOR NEWTON METHOD AND QUASI - NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEM

Abstract

The optimization problem has many effective and widespread applications in resource planning, machine design, automatic control, business administration, urban architecture that creating decision support systems in management and development of large systems. Nowadays, there are many effective algorithms published to solve optimization problems, including iterative algorithms such as Gradient algorithm, Newton’s algorithm and variations of this algorithm that are applied in learning machine, deep learning, regression,... In this paper, we introduce an algorithm based on Newton method and Quansi - Newton method, they are effective methods of finding solutions for optimal problems when the objective function is a convex, then we give some computing results for the algorithm to illustrate the convergence of the method.