Distributed Constrained Nonsmooth Minimax Optimization in Two Multiagent Systems: An Adaptive Penalty Approach

Area of Science:

• Optimization
• Distributed Systems
• Game Theory

Background:

• Minimax problems are crucial in various fields, but solving nonsmooth constrained variants remains challenging.
• Existing algorithms often struggle with distributed settings and partial agent knowledge.
• Nonsmooth convex-concave minimax problems with inequality constraints in multiagent systems are underexplored.

Purpose of the Study:

• To develop a distributed algorithm for nonsmooth constrained minimax optimization.
• To address challenges in multiagent systems with competing objectives and partial information.
• To create an adaptive strategy that avoids complex parameter estimation.

Main Methods:

• A distributed continuous-time penalty-based algorithm is proposed.
• The algorithm adaptively determines penalty gains, eliminating Lagrangian multiplier variables.
• It operates in multiagent systems where agents have partial knowledge of opposing subsystems.

Main Results:

• The algorithm achieves group consensus among agents.
• The state solution converges to the saddle point of the minimax problem.
• Numerical simulations validate the algorithm's effectiveness and superiority.

Conclusions:

• The proposed adaptive distributed algorithm effectively solves nonsmooth constrained minimax problems.
• It offers a robust solution for multiagent systems with competing objectives.
• The method demonstrates convergence to saddle points and superior performance over existing approaches.