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arXiv · 2010.09496

Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization

Adrian Hauswirth·Lukas Ortmann·Saverio Bolognani·Florian Dörfler
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Abstract

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.

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Adrian Hauswirth, Lukas Ortmann, Saverio Bolognani, Florian Dörfler. 2020-10-19. Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization. https://arxiv.org/abs/2010.09496

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