Fixed-Time Algorithms for Time-Varying Convex Optimization

To resolve the time-varying convex optimization problems with the cost function, the constraints or both being time dependent, in this brief we investigate a novel type of fixed-time algorithms. First, with the unconstrained time-varying optimization problem considered, a general framework algorithm is developed for tracking its optimal trajectory within fixed time, which contains the gradient flow-based scheme and Newton-type method as its special cases. Then, considering the equality constraint being involved in the time-varying optimization problem, we design another algorithm with fixed-time convergence, which includes Newton-type scheme as its special case. To verify that the given approach achieves fixed-time convergence, the simulation result is given with first-order Euler discretization.

Automated summary

In this paper, a novel type of fixed-time algorithms is investigated to solve time-varying convex optimization problems with time-dependent cost function, constraints or both. First, a general framework algorithm is developed for the unconstrained time-varying optimization problem to track its optimal trajectory within fixed time, which includes the gradient flow-based scheme and Newton-type method as special cases. Then, another algorithm with fixed-time convergence is designed for time-varying optimization problems involving equality constraint, including Newton-type scheme as a special case. The simulation result using first-order Euler discretization is provided to verify the fixed-time convergence achieved by the proposed approach.