An accelerated minimax algorithm for convex-concave saddle point problems with nonsmooth coupling function

Abstract In this work we aim to solve a convex-concave saddle point problem, where the coupling function is smooth in one variable and nonsmooth other not assumed be linear either. The problem augmented by regulariser component. We propose investigate novel algorithm under name of OGAProx , consisting an optimistic gradient ascent step coupled with proximal regulariser, which alternated component function. consider situations convex-concave, convex-strongly concave strongly related investigation. Regarding iterates obtain (weak) convergence, convergence rate order $$\mathcal {O}(\frac{1}{K})$$ O ( 1 K ) like {O}(\theta ^{K})$$ θ $$\theta < 1$$ < respectively. terms values ergodic rates {O}(\frac{1}{K^{2}})$$ 2 validate our theoretical considerations on nonsmooth-linear training multi kernel support vector machines classification incorporating minimax group fairness.