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Posted September 30, 2026

Control and Optimization Seminar Questions or comments?

Daniel Wachsmuth, University of Wuerzburg, Germany
Solution Algorithms for Nonsmooth Optimal Control Problems Based on the Pontryagin Maximum Principle

The talk is motivated by optimal control problems for partial differential equations. The main interest is in problems that involve integral functions of the type \[\int_\Omega g(u(x)) \ dx,\] where $g : \mathbb R \to \mathbb R$ is nonsmooth and nonconvex, and $u$ is the control variable. Examples involve $L^{\scriptscriptstyle r}$-pseudonorms with $r\in [0,1)$ or problems with the constraint $u(x) \in \mathbb Z$ for $x\in \Omega$. Due to the nonconvexity of $g$, the existence of solutions in $L^{\scriptscriptstyle p}$-spaces cannot be proven. Local solutions (if they exist) can be proven to satisfy the Pontryagin maximum principle. A distinctive feature of this result is that no differentiability with respect to the control variable $u$ is required. The maximum principle serves as a starting point to develop an implementable solution algorithm. We prove that the residual in the maximum principle vanishes along the iterates produced by the algorithm. Under additional assumptions, the iterates are a minimizing sequence.

Posted September 21, 2026

Control and Optimization Seminar Questions or comments?

Radu Bot, University of Vienna
TBA

Posted September 22, 2026

Control and Optimization Seminar Questions or comments?

Rene Henrion, Weierstrass Institute for Applied Analysis and Stochastics, Germany
TBA

Posted September 1, 2026

Control and Optimization Seminar Questions or comments?

Jun Liu, University of Waterloo, Canada
TBA