Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization
- Conference Paper
In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is either strictly convex in the primal or strictly concave in the dual variables. In this paper, we show convergence under non-strict convexity when a simple, unilateral augmentation term is added. For this purpose, we establish a novel, non-trivial characterization of the limit set of saddle-flow trajectories that allows us to preclude limit cycles. With our presentation we try to unify several existing problem formulations as a projected dynamical system that allows projection of both the primal and dual variables, thus complementing results available in the recent literature. Show more
Book title21th IFAC World Congress. Proceedings
Journal / seriesIFAC-PapersOnLine
Pages / Article No.
SubjectSaddle-point algorithms; Discontinuous systems; Convex optimization; Dynamical systems
Organisational unit09478 - Dörfler, Florian / Dörfler, Florian
09481 - Hug, Gabriela / Hug, Gabriela
160573 - Plug-and-Play Control & Optimization in Microgrids (SNF)
NotesDue to the Coronavirus (COVID-19) the 21st IFAC World Congress 2020 became the 1st Virtual IFAC World Congress (IFAC-V 2020).
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