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
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