Abstract: In this paper, combined exterior penalty function-conjugate gradient algorithm for a constrained optimal control problem for the coefficients of a quasilinear equation is applied. The constrained optimal control problem has been converted to one of the optimization problem using a penalty function technique. One of the approaches of building the gradient of the modified functional using the solving of the adjoint problem is investigated. A special case of the optimal control problem for the considering problem to illustrate the numerical results is investigated. The computing optimal controls are helped to identify the unknown coefficients of the quasilinear parabolic equation. The numerical results are presented.

Keywords: Optimal control, Quasilinear Parabolic Equation, Existence and Uniqueness Theorems, Adjoint system, Gradient formulae, Exterior penalty function-conjugate gradient algorithm.

ACM Classification Keywords: F.2.1 Numerical algorithm and problems,G.4 Mathematical Software

Link:

A COMBINED EXTERIOR PENALTY FUNCTION – CONJUGATE GRADIENT ALGORITHM FOR A CLASS OF CONSTRAINED OPTIMAL CONTROL QUASILINEAR PARABOLIC SYSTEMS

M. H. Farag and T. A. Talaat

http://www.foibg.com/ijita/vol20/ijita20-02-p03.pdf