Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"

Oberseminar , Nummer im Vorlesungsverzeichnis: 10525

SWS: 2

Dozenten

Mario Bebendorf, Kurt Chudej, Lars Grüne, Anton Schiela

Allgemeines

gemeinsames Oberseminar der Lehrstühle für Angewandte Mathematik und Wissenschaftliches Rechnen

Vortragsankündigungen für das Oberseminar

Im Rahmen unseres gemeinsamen Oberseminars findet folgender virtueller Vortrag statt:

Am Montag, dem 13. Juli 2020, um 16:00 Uhr im Zoom-Meeting, spricht

Herr B.S. Sungho Shin
Scalable Systems Laboratory
Department of Chemical and Biological Engineering
College of Engineering
University of Wisconsin-Madison, Madison, Wisconsin, USA

über das Thema
"Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs"

Abstract:

In this talk, I will discuss solution sensitivity for nonlinear programs whose structure is induced by a graph. These graph-structured problems arise in applications such as optimal control, stochastic optimization, optimization with partial differential equations, and network optimization. I will show that the sensitivity of the primal-dual solution against a data perturbation is bounded by a term that decreases exponentially in the distance to the perturbation point. Remarkably, this result (which we call exponential decay of sensitivity) holds under fairly standard assumptions used in classical sensitivity theory: second-order sufficiency conditions, the linear independence constraint qualification, and strict complementarity. I will also present conditions under which the constants in the exponential estimate remain uniformly bounded; this allows us to characterize behavior for problems defined over infinite graphs (e.g., arising from the discretization of infinite-dimensional problems). Our results provide new insights on how perturbations propagate through graphs and on how the NLP formulation influences such propagation. In the later part of the talk, I will discuss applications of exponential decay of sensitivity in creating efficient computing strategies. In particular, the overlapping Schwarz decomposition method and diffusing-horizon model predictive control will be discussed.

Einladende:

Prof. Dr. Mario Bebendorf
Prof. Dr. Kurt Chudej
Prof. Dr. Lars Grüne
Prof. Dr. Anton Schiela

Lehrstuhl -

|  Universität Bayreuth -