In this paper, a distributed neurodynamic optimization method is developed for a class of multicluster resource allocation models with 0-1 integer constraints and cardinality constraints. In the optimization model, the objective function is the sum of multiple clusters of convex local objective functions with 0-1 integer constraints that lead to nonconvexity; additionally, the resource allocation model is subject to globally coupled resource allocation constraints and bound constraints, and the cardinality constraints are introduced to limit the total number of resource-allocated points in each cluster. To address challenges caused by the nonconvexity and hybrid constraints, a distributed neurodynamic optimization method based on an augmented Lagrangian function is developed, and it is proven to converge to a local minimum. The validity of the main results is demonstrated via two examples involving a power system.

In this article, two types of multiagent systems (MASs) are developed for distributed bilevel constrained optimization. Within the framework of the distributed bilevel optimization modeling, the objective function is in a summation manner of local objective functions. Multiple agents connected via a communication network are harnessed for optimizing the local objective functions cooperatively while adhering to coupled constraints with global information, and each agent is tasked with solving an individual inner problem and it is subject to multiple local constraints. To address challenges posed by the distributed computation requirement of the proposed bilevel optimization models and multiple complex constraints, first and second-order MASs are customized and proven to converge to the optimal solution. Three examples involving two numerical simulations and an economic dispatch problem are elaborated to verify and demonstrate the optimality, enhanced robustness to communication blocking, and fast convergence of the proposed approaches.

In this article, a momentum-based multiagent optimization approach is developed for distributed nonconvex optimal resource allocation. The proposed resource allocation model is formulated without the convex conditions, and a paradigmatic system based on the gradient descent with momentum method is proposed for handling its functional nonconvexity. Based on the paradigmatic system, a momentum-based multiagent system (MAS) is developed, and its convergence and convergence rate to a local minimizer are proven. Then, a distributed average tracking approach is introduced, based on which a hybrid multiagent optimization approach consisting of multiple MASs and a meta-heuristic rule is designed for seeking global minimizers. Finally, a simulation in a chiller system is elaborated to demonstrate the enhanced stability, fast convergence, and optimality of the developed distributed optimization approaches.

In this article, we propose a collaborative neurodynamic optimization (CNO) method for the distributed seeking of generalized Nash equilibriums (GNEs) in multicluster games with nonconvex functions. Based on an augmented Lagrangian function, we develop a projection neural network for the local search of GNEs, and its convergence to a local GNE is proven. We formulate a global optimization problem to which a global optimal solution is a high-quality local GNE, and we adopt a CNO approach consisting of multiple recurrent neural networks for scattering searches and a metaheuristic rule for reinitializing states. We elaborate on an example of a price-bidding problem in an electricity market to demonstrate the viability of the proposed approach.

In this paper, we address matrix-valued distributed stochastic optimization with inequality and equality constraints, where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner. A penalty method is derived to deal with the constraints, and a selection principle is proposed for choosing feasible penalty functions and penalty gains. A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem, and its convergence to the optimal solution is analyzed rigorously. Two numerical examples are given to demonstrate the viability of the main results.

In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.

This technical note proposes a decentralized-partial-consensus optimization (DPCO) problem with inequality constraints. The partial-consensus matrix originating from the Laplacian matrix is constructed to tackle the partial-consensus constraints. A continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the optimization problem. In addition, based on nonsmooth analysis and Lyapunov theory, the convergence of continuous-time algorithm is further proved. Finally, several examples demonstrate the effectiveness of main results.

In this article, we present a collaborative neurodynamic approach to distributed optimization with nonconvex functions. We develop a recurrent neural network (RNN) group by connecting individual projection neural networks through a communication network. We prove the convergence of the RNN group to the local optimal solutions of a given distributed optimization problem. We propose a collaborative neurodynamic optimization system with multiple RNN groups for scattered searches and a metaheuristic rule for reinitializing the neuronal states upon their local convergence. We elaborate on three numerical examples to demonstrate the efficacy of the proposed approach to distributed global optimization in the presence of nonconvexity.

This article focuses on a distributed optimization problem subject to partial-impact cost functions that relates to two decision variable vectors. To this end, two algorithms are presented with the aim of solving the considered optimization problem in a structure fashion and in a gradient fashion, respectively. Furthermore, a connection between the equilibrium of the induced algorithm and the involved optimization problem is established, with the aid of the tools from nonsmooth analysis and change of coordinate theorem. Two numerical examples with practical significance are given to demonstrate the efficiency of the designed algorithm.

This article studies the constrained optimization problems in the quaternion regime via a distributed fashion. We begin with presenting some differences for the generalized gradient between the real and quaternion domains. Then, an algorithm for the considered optimization problem is given, by which the desired optimization problem is transformed into an unconstrained setup. Using the tools from the Lyapunov-based technique and nonsmooth analysis, the convergence property associated with the devised algorithm is further guaranteed. In addition, the designed algorithm has the potential for solving distributed neurodynamic optimization problems as a recurrent neural network. Finally, a numerical example involving machine learning is given to illustrate the efficiency of the obtained results.