A Predefined-Time Adaptive Algorithm for Optimization Problems

This paper proposes a predefined-time adaptive algorithm for the optimization problem with private inequality constraints. By designing algorithms, penalty parameters are designed to handle private inequality constraints, and through adaptive penalties, the parameters in the algorithm are adaptively adjusted according to the degree of violation of private inequality constraints by the state solution. Moreover, The smoothing method is also integrated into adaptive penalty, overcoming the difficulty of non smooth dynamic behavior of the objective function and adaptive penalty parameters. In addition, a predefined-time mechanism is introduced to enable the algorithm to converge within the predefined-time.