A fixed-time gradient algorithm for distributed optimization with inequality constraints

Abstract

In this paper, a distributed fixed time gradient algorithm for neurodynamic systems is proposed for solving optimization problems with local inequality constraints. The algorithm is designed using fixed time theory and sliding model control techniques, where each agent has a local objective function known only to itself, and the optimal solution of each local objective function sum can be obtained in a fixed time by the information interaction between neighbors under the condition of local inequality constraints. In addition, the upper bound of the fixed time can be obtained and it is proved theoretically that the upper bound of the fixed time is independent of the initial value. Finally, the stability and effectiveness of the algorithm are verified by numerical examples.