Initialization-free optimization algorithm for interval-valued distributed optimization

This paper introduces an initialization-free optimization algorithm for nonsmooth interval-valued distributed optimization problems (IV-DOPs), aimed at addressing the challenge of inaccurate system parameter measurements commonly encountered in engineering applications. Acknowledging the inherent presence of external interference in practical network systems, the proposed optimization algorithm is combined with sliding mode technology and is able to suppress the interference in a prescribed time instant. To deal with partial order inequality constraints and set constraints of the concerned IV-DOP, projection operators and the adaptive penalty method are integrated into the optimization algorithm for the first time. Furthermore, the effectiveness of the proposed optimization algorithm without initialization is analyzed. Finally, two numerical simulations are implemented to demonstrate the effectiveness of the proposed projection-based adaptive optimization algorithm.