An Adaptive Optimization Algorithm for Heterogeneous Linear Multi-Agent Systems with Inequality Constraints

This paper considers a distributed constrained optimization problem for heterogeneous linear multi-agent systems over weight-unbalanced digraphs. Each agent only uses local information under the local convex function inequality constraints such that all agents can achieve the optimal output of the global objective function, consisting of strongly convex objective functions with globally Lipschitz gradients. Firstly, a distributed adaptive optimization algorithm is proposed that removes the requirement of any global information. Secondly, based on the Karush-Kuhn-Tucker(KKT) condition and Lyapunov stability, the asymptotical convergence of the proposed algorithm is proved. Finally, a numerical example is given to illustrate the results.