A Consecutive Quasilinearization Method for the Optimal Boundary Control of Semilinear Parabolic EquationsReportar como inadecuado




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Optimal boundary control of semilinear parabolicequations requires efficient solution methods in applications. Solution methodsbypass the nonlinearity in different approaches. One approach can bequasilinearization QL but its applicability is locally in time. Nonetheless,consecutive applications of it can form a new method which is applicable globallyin time. Dividing the control problem equivalently into many finite consecutivecontrol subproblems they can be solved consecutively by a QL method. Theproposed QL method for each subproblem constructs an infinite sequence oflinear-quadratic optimal boundary control problems. These problems havesolutions which converge to any optimal solutions of the subproblem.This implies the uniqueness of optimal solution to the subproblem. Mergingsolutions to the subproblems the solution of original control problem isobtained and its uniqueness is concluded. This uniqueness result is new. Theproposed consecutive quasilinearization method is numerically stable withconvergence order at least linear. Its consecutive feature prevents large scale computations andincreases machine applicability. Its applicability for globalization of locallyconvergent methods makes it attractive for designing fast hybrid solutionmethods with global convergence.

KEYWORDS

Quasilinearization; Optimal Boundary Control; SQP Methods; Semilinear Parabolic PDE’s

Cite this paper

Nayyeri, M. and Kamyad, A. 2014 A Consecutive Quasilinearization Method for the Optimal Boundary Control of Semilinear Parabolic Equations. Applied Mathematics, 5, 691-706. doi: 10.4236-am.2014.54067.





Autor: Mohammad Dehghan Nayyeri, Ali Vahidian Kamyad

Fuente: http://www.scirp.org/



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