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Article citations


Raymond, J.P. and Zidani, H. (1999) Hamiltonian Pontryagin’s Principles for Control Problems Governed by Semilinear Parabolic Equations. Applied Mathematics and Optimization, 39, 143-177.

has been cited by the following article:

  • 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.