Recent Results on Second Order Optimality Conditions in Control of Partial Differential Equations

E. Casas Rentería

In this talk, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed. The cost functional involves the state and possibly a sparsity-promoting term, but not a Tikhonov regularization term. Unlike finite dimensional optimization or control problems involving Tikhonov regularization, second order sufficient optimality conditions for the problems we deal with, must be imposed in a cone larger than the one used to obtain necessary conditions. Different extensions of this cone have been proposed in the literature for different kinds of minima, namely strong or weak minimizers for optimal control problems. We propose a new extended cone, smaller than those considered until now, and prove that a second order condition based on this new cone is sufficient for a strong local minimum.

Keywords: optimal control, parabolic equations, second order conditions, sparse controls

GT11-2 MA-2 Continuous Optimization. Tribute to Marco Antonio López
September 5, 2019  4:05 PM
I2L7. Georgina Blanes building

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