Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM

Abstract

In this paper, a class of Nonlinear Programming problem is modeled with gradient basedsystem of fractional order differential equations in Caputo's sense. To see the overlap between theequilibrium point of the fractional order dynamic system and the optimal solution of the NLP problemin a longer timespan the Multistage Variational teration Method is applied. The comparisons amongthe multistage variational iteration method, the variational iteration method and the fourth orderRunge-Kutta method in fractional and integer order show that fractional order model and techniquescan be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programmingproblems.

In this paper, a class of Nonlinear Programming problem is modeled with gradient basedsystem of fractional order differential equations in Caputo's sense. To see the overlap between theequilibrium point of the fractional order dynamic system and the optimal solution of the NLP problemin a longer timespan the Multistage Variational teration Method is applied. The comparisons amongthe multistage variational iteration method, the variational iteration method and the fourth orderRunge-Kutta method in fractional and integer order show that fractional order model and techniquescan be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programmingproblems.