Gradient descent method for unconstrained minimax problem based on max(0,x) aggregate smoothing

Based on the aggregate smoothing of max(0,x), a smooth gradient descent method for unconstrained minimax problem is proposed. Firstly, the unconstrained minimax problem is transformed into an equivalent non-smooth problem containing max(0,x) function. The unconstrained smooth optimization problem is obtained by the aggregate smoothing approximation technique. Through the numerical experiments of three examples, compared with two typical algorithms, the proposed algorithm shows good competitiveness.