An optimal algorithm for minimax problems with smooth components

Abstract

In this paper, we propose an optimal algorithm for the convex minimax. This is an extension of the Nestrerov algorithm, which allows step size parameters to be non-constant and determined automatically during algorithm execution. We present the algorithm and prove the convergence of this algorithm with the optimal order. To calculate the gradient mapping, we apply the external point penalty function method. We then propose a method of determining the parameters in the algorithm automatically. The proposed new algorithm, which is integrated with the method of calculating gradient mapping and automatic parameter determination, is detailed in Algorithm 6.1. Finally, we applied the new algorithm to solve some specific examples and compared it with Nesterov's algorithm.

Keywords

• minimax optimal problem
• optimal algorithm
• nesterov’s algorithm
• convergence
• optimal convergence rate