Numerical Solutions for the Optimal Control Governing by Variable Coefficients Nonlinear Hyperbolic Boundary Value Problem Using the Gradient Projection, Gradient and Frank Wolfe Methods

  • Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Eman H. Mukhalef Al-Rawdanee Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Keywords: Numerical Classical Optimal Control, Galerkin Finite Element Method, Gradient Method, Gradient Projection Method, Frank Wolfe Method

Abstract

This paper is concerned with studying the numerical solution for the discrete classical optimal control problem (NSDCOCP) governed by a variable coefficients nonlinear hyperbolic boundary value problem (VCNLHBVP). The DSCOCP is solved by using the Galerkin finite element method (GFEM) for the space variable and implicit finite difference scheme (GFEM-IFDS) for the time variable to get the NS for the discrete weak form (DWF) and for the discrete adjoint weak form (DSAWF) While, the gradient projection method (GRPM), also called the gradient method (GRM), or the Frank Wolfe method (FRM) are used to minimize the discrete cost function (DCF) to find the DSCOC. Within these three methods, the Armijo step option (ARMSO) or the optimal step option (OPSO) are used to improve the discrete classical control (DSCC). Finally, some illustrative examples for the problem are given to show the accuracy and efficiency of the methods.

Published
2020-05-17
How to Cite
Al-HawasyJ. A. A., & Al-RawdaneeE. H. M. (2020). Numerical Solutions for the Optimal Control Governing by Variable Coefficients Nonlinear Hyperbolic Boundary Value Problem Using the Gradient Projection, Gradient and Frank Wolfe Methods. Iraqi Journal of Science, 161-169. https://doi.org/10.24996/ijs.2020.SI.1.21