Distributed Interval Optimization Over Time-Varying Networks: A Numerical Programming Perspective

In this study, we investigate a distributed interval optimization problem involving agents linked by a time-varying network, optimizing interval objective functions under global convex constraints. Through scalarization, we first reformulate the distributed interval optimization problem as a distributed constrained optimization problem. The optimal Pareto solutions to the reformulated problem are then illustrated. We establish a distributed subgradient-free algorithm for the distributed constrained optimization problems by generating random differences of reformulated optimal objective functions, and the optimal solutions of the distributed constrained optimization problem are equivalent to Pareto optimal solutions of the distributed interval optimization problem. Moreover, we demonstrate that a Pareto optimal solution can be reached over the time-varying network using the proposed algorithm almost surely. FInally, we conclude with a numerical simulation to demonstrate the effectiveness of the proposed algorithm.