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Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems

Author

Listed:
  • Ali Lotfi

    (Shahid Beheshti University, G.C)

  • Sohrab Ali Yousefi

    (Shahid Beheshti University, G.C)

Abstract

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique.

Suggested Citation

  • Ali Lotfi & Sohrab Ali Yousefi, 2014. "Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 884-899, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-013-0511-5
    DOI: 10.1007/s10957-013-0511-5
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    Cited by:

    1. Ali Lotfi, 2017. "A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 65-82, July.
    2. Teodor M. Atanacković & Marko Janev & Stevan Pilipović & Dušan Zorica, 2017. "Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 256-275, July.
    3. Araz Noori Dalawi & Mehrdad Lakestani & Elmira Ashpazzadeh, 2022. "An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    4. Ali Lotfi & Sohrab Ali Yousefi, 2017. "A Generalization of Ritz-Variational Method for Solving a Class of Fractional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 238-255, July.

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