| MS Seminar

Name of the Speaker: Ms. Swetha Avulapati (EE21S203)
Guide: Dr. Arunkumar D Mahindrakar
Online meeting link: https://meet.google.com/kfx-cxnw-skv
Date/Time: 13th May 2025 (Tuesday), 10:00 AM
Title: A Dynamical Systems Approach to Solve Inequality Constrained Distributed Convex Optimization on General Digraph.

Abstract :

Solving a distributed optimization problem generally involves studying the asymptotic stability to the set of optimizers of the optimization problem. One of the approaches for the same is the use of continuous-time dynamical systems, particularly saddle-point dynamics. In certain scenarios, these dynamics are a modified version of saddle-point dynamics adapted according to the respective optimization problem. For instance, this modified nature of the dynamics is evident for unconstrained optimization problems on strongly-connected, weight-balanced digraphs. In our research, we propose a novel modified saddle-point dynamics designed to solve inequality-constrained optimization problems over strongly-connected general (weight-unbalanced) digraphs. To address the challenges posed by such general digraphs, we propose a novel continuous-time weight-balancing dynamics (digraph topology unaltered), with each iterate of the weights simultaneously used to solve the remainder of the saddle-point dynamics involving projection-based non-smooth nature for inequality constraints. To analyze the stability of our proposed dynamical system, we first show that the weight-balancing dynamics exponentially converge to steady-state weights that weight-balance the digraph. We subsequently show that the optimal solution for the general digraphs are the Lyapunov stable equilibrium points for the proposed overall dynamics. Lastly, we prove that every trajectory of the proposed dynamics converges asymptotically to an equilibrium point.