2020/10/19 by Adrian Hauswirth, Lukas Ortmann, Hauswirth, Adrian +5
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2010.09496
openalex publication_date 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the stability and convergence of continuous-time\nLagrangian saddle flows to solutions of a convex constrained optimization\nproblem. Convergence of these flows is well-known when the underlying saddle\nfunction is either strictly convex in the primal or strictly concave in the\ndual variables. In this paper, we show convergence under non-strict convexity\nwhen a simple, unilateral augmentation term is added. For this purpose, we\nestablish a novel, non-trivial characterization of the limit set of saddle-flow\ntrajectories that allows us to preclude limit cycles. With our presentation we\ntry to unify several existing problem formulations as a projected dynamical\nsystem that allows projection of both the primal and dual variables, thus\ncomplementing results available in the recent literature.\n