A New Approach for Solving Minimax Problems Using New Generation Smoothing Techniques

This study focuses on solving finite minimax problems. A new reformulation for the minimax problems is established based on indicator functions. The relations between the original and reformulated problems are investigated. Based on the new formulation of minimax problems, a new smoothing approach is proposed via the approximation of the indicator functions. A new algorithm is developed to solve the reformulated and smoothed problems. Finally, the performance of the algorithm is illustrated on some test problems, and the comparison of the obtained numerical results with the other methods is presented.