Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems |
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Authors: | Hans D Mittelmann |
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Institution: | (1) Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804, USA |
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Abstract: | We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before. |
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Keywords: | elliptic and parabolic control problems control and state constraints second-order sufficient conditions discretizations optimization methods |
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