Abstract
In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational ?teration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.
Highlights
Many problems in modern science and technology are commonly encountered with some class of optimization problems
The main idea behind the method is to replace optimization problem to a system of ordinary differential equations (ODEs), which is equipped with optimality conditions, for getting optimal solutions of the nonlinear programming (NLP) problem
The intersection point is composed through the instrument of fractional order differential equations (FDEs) system
Summary
Many problems in modern science and technology are commonly encountered with some class of optimization problems. Gradient based method is one of these approaches for solving NLP problems. Most of the studies in this area have mainly focused on developing analytical and numerical methods for solving different kind of fractional differential equations (FDEs) in science. Multistage technique is adapted to the VIM for getting the essential behavior of the differential equation system for large time t This technique was introduced by Batiha et al [28] for a class of nonlinear system of ODEs and applied to delay differential equations by Gokdogan [29]. We construct a fractional gradient based system for solving equality constrained optimization problem. Any limit point of the sequence is a solution to the constrained problem
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