An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

Mehmet Yavuz,Fırat Evirgen

doi:10.1051/itmconf/20182201009

Abstract

In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

Highlights

Optimization theory and fractional calculus are the essential elements of the mathematical modeling process
The solution process is generated with the help of a differential equation system which includes optimality conditions
A mathematical model, which is constructed by using the Caputo-Fabrizio fractional derivative, is handled for determining the optimal solutions of (2), and of the equality constrained optimization problem (1) with the help of the multistage variational iteration method (MVIM)

Summary

Introduction

Optimization theory and fractional calculus are the essential elements of the mathematical modeling process. The fractional calculus topics are drawn increasing attention from the researchers as it has a capability of representing real-world problems better than regular derivative In this sense, various types of fractional derivatives, integrals, and applications are introduced by scientists. Podlubny [6] and Baleanu et al [7] provided comprehensive discussions on these definitions In their recent work, Caputo and Fabrizio [8] introduced a new derivative of fractional order with a nonsingular kernel. We will investigate the solution procedure of the optimization problems with the constructed mathematical model by Caputo-Fabrizio fractional derivative operator. Any accumulation points of the sequence are the solution of the original constrained problem (1)

Caputo-Fabrizio fractional derivative

Variational iteration method

A mathematical model involving Caputo-Fabrizio derivative

Numerical simulations

Conclusion