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Sufficient Optimality in a Parabolic Control Problem

Hans D. Mittelmann (mittelmann***at***asu.edu)
Fredi Troeltzsch (troeltz***at***math.tu-berlin.de)

Abstract: We define a class of parabolic problems with control and state constraints and identify a problem within this class which possesses a locally unique critical point satisfying the second order sufficient optimality conditions. In this solution inequality constraints on the control are strongly active. The second derivative of the Lagrangian is not globally coercive. This is both shown analytically as well as verified numerically for a finite difference discretization.

Keywords: Optimal control, nonlinear parabolic equation, second-order sufficient optimality condition, numerical verification

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: in "Trends in Industrial Mathematics", Applied Optimization, vol. 72, A.H. Siddiqi and M. Kocvara (eds), Kluwer, Dordrecht, The Netherlands, 2002

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Entry Submitted: 07/22/2001
Entry Accepted: 07/23/2001
Entry Last Modified: 11/12/2002

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