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Daily Overview |
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OC1: Optimisation and Control Location: A702 Session Chair: Behzad Azmi | |
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On Quantitative Sufficient Second-Order Optimality Conditions for Elliptic Optimal Control Problems Universität Tübingen, Germany We consider distributed optimal control problems with box constraints governed by a semilinear elliptic equation and without Tikhonov regularization. In this setting, the second variation is a quadratic form in the linearized state, and its curvature function may vanish or change sign. We derive quantitative conditions on the adjoint state that imply coercivity of the second variation with respect to the L²-norm of the linearized state on an extended critical cone. The analysis relies on estimates for solutions of the homogeneous linearized equation on superlevel sets of the adjoint state. We also show that this second-order condition is stable under perturbations of the state and the tracking data. This talk is based on joint work with Francisco Fuica. | |
