Sign Hessian-Weighted Gradient Algorithms for Distributed Time-Varying Convex Optimization

In this article, we initiate our exploration with a time-varying optimization problem, featuring linear equality constraints. To address this complex problem, we introduce a novel continuous-time sign Hessian-weighted gradient algorithm. Remarkably, our proposed approach is capable of handling the time-varying nature of the problem, all without the need for the invertibility of the Hessian matrix associated with the cost function. We present two distinct distributed algorithms: the edge-based and node-based variations. To underscore the practical effectiveness of our methodology, we provide some numerical examples, offering compelling evidence to validate our research findings.