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Distributed optimization has gained significant attention in recent years,primarily fueled by the availability of a large amount of data andprivacy-preserving requirements. This paper presents a fixed-time convergentoptimization algorithm for solving a potentially non-convex optimizationproblem using a first-order multi-agent system. Each agent in the network canaccess only its private objective function, while local information exchange ispermitted between the neighbors. The proposed optimization algorithm combines afixed-time convergent distributed parameter estimation scheme with a fixed-timedistributed consensus scheme as its solution methodology. The results arepresented under the assumption that the team objective function is stronglyconvex, as opposed to the common assumptions in the literature requiring eachof the local objective functions to be strongly convex. The results extend tothe class of possibly non-convex team objective functions satisfying only thePolyak-\L ojasiewicz (PL) inequality. It is also shown that the proposedcontinuous-time scheme, when discretized using Euler's method, leads toconsistent discretization, i.e., the fixed-time convergence behavior ispreserved under discretization. Numerical examples comprising large-scaledistributed linear regression and training of neural networks corroborate ourtheoretical analysis.

Accelerating Distributed Optimization via Fixed-time Convergent Flows: Extensions to Non-convex Functions and Consistent Discretization