An adaptive nonmonotone Barzilai-Borwein gradient method for the optimal control of Burgers equation

This paper attempts to present a nonlinear optimization method to find the optimal control of Burgers equation with a quadratic cost functional. The discretize-then-optimize approach is used. Afterward, regarding the implicit function theorem (IFT), the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Also, to make a globalization strategy, an adaptive nonmonotone strategy which properly controls the degree of nonmonotonicity is used and is incorporated into an inexact Armijo-type line search approach to construct a more relaxed line search procedure. Finally, the obtained UNOP is solved by utilizing the proposed nonmonotone Barzilai-Borwein gradient method. Results gained from the new offered method show that the new method is promising.