Solving specified-time distributed optimization problem with local inequality constraint based on penalty method

This paper focuses on solving distributed optimization problems with local nonlinear inequality constraints in a specified-time over undirected graph. Here, we present a distributed optimization algorithm with specified-time. It can be used for the multi-agent network to minimize the sum of local objective functions. The establishment of specified-time in the proposed algorithm is independent of initial conditions and algorithm parameters. This is a completely distributed algorithm, which only needs information interaction between adjacent agents to complete the specified-time optimization problem. The effectiveness of the proposed theory is demonstrated by an example of resource allocation.