Network Optimization via Smooth Exact Penalty Functions Enabled by Distributed Gradient Computation

This article proposes a distributed algorithm for network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained as unconstrained smooth (continuously differentiable) exact penalty function. Computing gradient this in way challenging even under separability assumptions problem. technical approach shows that computation can be formulated system linear algebraic equations defined by data. To it, we design exponentially fast, input-to-state stable does not require individual agent matrices invertible. We employ compute at current state. algorithmic solver interconnects estimation prescription having follow resulting direction. Numerical simulations illustrate convergence robustness properties proposed algorithm.