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Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems

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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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  1. Department of Mathematics, Arizona State University, Tempe, Arizona, 85287-1804, USA

    Hans D. Mittelmann

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  1. Hans D. Mittelmann
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Mittelmann, H.D. Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems. Computational Optimization and Applications 20, 93–110 (2001). https://doi.org/10.1023/A:1011275507262

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