  Distributed optimization has gained significant attention in recent years,
primarily fueled by the availability of a large amount of data and
privacy-preserving requirements. This paper presents a fixed-time convergent
optimization algorithm for solving a potentially non-convex optimization
problem using a first-order multi-agent system. Each agent in the network can
access only its private objective function, while local information exchange is
permitted between the neighbors. The proposed optimization algorithm combines a
fixed-time convergent distributed parameter estimation scheme with a fixed-time
distributed consensus scheme as its solution methodology. The results are
presented under the assumption that the team objective function is strongly
convex, as opposed to the common assumptions in the literature requiring each
of the local objective functions to be strongly convex. The results extend to
the class of possibly non-convex team objective functions satisfying only the
Polyak-\L ojasiewicz (PL) inequality. It is also shown that the proposed
continuous-time scheme, when discretized using Euler's method, leads to
consistent discretization, i.e., the fixed-time convergence behavior is
preserved under discretization. Numerical examples comprising large-scale
distributed linear regression and training of neural networks corroborate our
theoretical analysis.
