A Finite-Time Consensus Continuous-Time Algorithm for Distributed Pseudoconvex Optimization With Local Constraints

In this article, we develop a continuous-time algorithm based on a multiagent system for solving distributed, nonsmooth, and pseudoconvex optimization problems with local convex inequality constraints. The proposed algorithm is modeled by differential inclusion, which is based on the penalty method...

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Veröffentlicht in:	IEEE transactions on automatic control Jg. 70; H. 2; S. 979 - 991
Hauptverfasser:	Wang, Sijian, Yu, Xin
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.02.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Constraints Continuous time systems Convex functions Distributed optimization finite-time consensus Heuristic algorithms Linear programming Multi-agent systems Multiagent systems Operators (mathematics) Optimization pseudoconvex optimization Recurrent neural networks Vectors
ISSN:	0018-9286, 1558-2523
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Abstract	In this article, we develop a continuous-time algorithm based on a multiagent system for solving distributed, nonsmooth, and pseudoconvex optimization problems with local convex inequality constraints. The proposed algorithm is modeled by differential inclusion, which is based on the penalty method rather than the projection method. Compared with existing methods, the proposed algorithm has the following advantages. First, this algorithm can solve the distributed optimization problem, in which the global objective function is pseudoconvex and the local objective functions are subdifferentially regular in the global feasible region; Moreover, each agent can have different constraints. Second, this algorithm does not require exact penalty parameters or projection operators. Third, the subgradient gains for different agents may be nonuniform. Fourth, all agents reach a consensus in finite time. It is proven that under certain assumptions, from an arbitrary initial state, the solutions of all the agents will enter their local inequality feasible region and remain there, reach consensus in finite time, and converge to the optimal solution set of the primal distributed optimization problem. Numerical experiments show that the proposed algorithm is effective.
AbstractList	In this article, we develop a continuous-time algorithm based on a multiagent system for solving distributed, nonsmooth, and pseudoconvex optimization problems with local convex inequality constraints. The proposed algorithm is modeled by differential inclusion, which is based on the penalty method rather than the projection method. Compared with existing methods, the proposed algorithm has the following advantages. First, this algorithm can solve the distributed optimization problem, in which the global objective function is pseudoconvex and the local objective functions are subdifferentially regular in the global feasible region; Moreover, each agent can have different constraints. Second, this algorithm does not require exact penalty parameters or projection operators. Third, the subgradient gains for different agents may be nonuniform. Fourth, all agents reach a consensus in finite time. It is proven that under certain assumptions, from an arbitrary initial state, the solutions of all the agents will enter their local inequality feasible region and remain there, reach consensus in finite time, and converge to the optimal solution set of the primal distributed optimization problem. Numerical experiments show that the proposed algorithm is effective.
Author	Yu, Xin Wang, Sijian
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SubjectTerms	Algorithms Constraints Continuous time systems Convex functions Distributed optimization finite-time consensus Heuristic algorithms Linear programming Multi-agent systems Multiagent systems Operators (mathematics) Optimization pseudoconvex optimization Recurrent neural networks Vectors
Title	A Finite-Time Consensus Continuous-Time Algorithm for Distributed Pseudoconvex Optimization With Local Constraints
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