TITLE:
A Consecutive Quasilinearization Method for the Optimal Boundary Control of Semilinear Parabolic Equations
AUTHORS:
Mohammad Dehghan Nayyeri, Ali Vahidian Kamyad
KEYWORDS:
Quasilinearization; Optimal Boundary Control; SQP Methods; Semilinear Parabolic PDE’s
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.4,
March
10,
2014
ABSTRACT: Optimal boundary control of semilinear parabolic
equations requires efficient solution methods in applications. Solution methods
bypass the nonlinearity in different approaches. One approach can be
quasilinearization (QL) but its applicability is locally in time. Nonetheless,
consecutive applications of it can form a new method which is applicable globally
in time. Dividing the control problem equivalently into many finite consecutive
control subproblems they can be solved consecutively by a QL method. The
proposed QL method for each subproblem constructs an infinite sequence of
linear-quadratic optimal boundary control problems. These problems have
solutions which converge to any optimal solutions of the subproblem.
This implies the uniqueness of optimal solution to the subproblem. Merging
solutions to the subproblems the solution of original control problem is
obtained and its uniqueness is concluded. This uniqueness result is new. The
proposed consecutive quasilinearization method is numerically stable with
convergence order at least linear. Its consecutive feature prevents large scale computations and
increases machine applicability. Its applicability for globalization of locally
convergent methods makes it attractive for designing fast hybrid solution
methods with global convergence.