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Unconstrained quadratic optimization problems are a common mathematical challenge encountered in various domains. These problems involve optimizing quadratic functions without explicit constraints. In a distributed computing environment, solving these optimization problems collectively among multiple computational nodes is a complex and crucial task. This paper introduces a distributed algorithm within a multi-agent framework that aims to find the global minimizer for such problems. The proposed algorithm demonstrates exponential convergence, assuming a static and connected communication network. Additionally, numerical simulations are conducted to support the theoretical findings. • A distributed algorithm is devised to solve the convex quadratic optimization problem. • The algorithm leverages the concept of strong duality in its development. • The technique solves QP over undirected multi-agent networks without exchanging minimizer estimates. • The algorithm achieves rapid, exponential convergence towards the global optimizer. • Simulation studies confirm the theoretical claims. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a distributed algorithm that is specifically designed to tackle the least-squares problem within a network system of linear algebraic equations. Our focus is on static directed multi-agent networks, where each agent possesses knowledge of a distinct subset of the linear equations. Furthermore, we examine a scenario where agents lack information about their "out-degrees" at any given time. By imposing the strong connectivity condition on the communication network, we establish that the local estimated solution of each agent exhibits exponential convergence towards the least-squares solution of the corresponding network system of linear algebraic equations. • A consensus based distributed algorithm is devised to solve the least-squares problem. • The technique solves LS estimation over directed networks where agents lack out-degree info. • Achieves rapid exponential convergence to the least-squares solution. • Simulation confirms algorithm's theory, shows improvements over existing methods. [ABSTRACT FROM AUTHOR]