Fixed-Time Distributed Strategy for Constrained Optimization

This paper focuses on the distributed strategy synthesis to tackle the collaborative optimization problem subject to general set constraints in fixed time. Distinct from the traditional collaborative optimization problem that requires local value functions and their sum being convex, no convexity requirement is essential herein. Besides, the underlying communication network is switching. By bringing in appropriate auxiliary mechanism, a fixed-time distributed optimization strategy is synthesized first. Then, under the assumptions that the sum of the local value functions is gradient dominated and the communication topology keeps connected, it is demonstrated that the synthesized distributed strategy in terms of proper parameter criteria is capable of calculating the expected optimal solution to the studied constrained optimization problem in initialization-free fixed time. Finally, examples are simulated to confirm the theoretical results.