Distributed Constrained Optimization with Uncoordinated Step Sizes: A Case Study on Ethylene Plant

This paper investigates an uncoordinated step sizes distributed optimization algorithm based on an undirected topology network structure, which can handle distributed optimization problems with inequality constraints and heterogeneity (losing the global clock) by only communicating with neighboring nodes. Firstly, an “Adapt-Then-Combine Distributed Inexact Gradient tracking subject to Inequality Constraints (ATC-DIGing-IC)” algorithm is proposed for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex>-strongly convex and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l$</tex>-smooth objective functions. Using the “Adapt-Then-Combine (ATC)” framework and the gradient information tracking structure, the flexibility and fastness of the algorithm can be guaranteed under the uncoordinated step size. Then, a parameter projection technique is introduced to handle the inequality constraints without introducing additional auxiliary variables. Subsequently, the convergence results of the algorithm and the bounds on the uncoordinated step sizes are theoretically analyzed. Finally, the algorithm is applied to a plant-wide separation production process of an ethylene plant, and the experimental results show that the proposed algorithm requires a shorter optimization time than the existing methods.