# A Primal-Dual Algorithm for General Convex-Concave Saddle Point Problems

@article{Hamedani2018APA, title={A Primal-Dual Algorithm for General Convex-Concave Saddle Point Problems}, author={Erfan Yazdandoost Hamedani and Necdet Serhat Aybat}, journal={arXiv: Optimization and Control}, year={2018} }

In this paper we propose a primal-dual algorithm with a momentum term that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle point problems defined by a convex-concave function $\mathcal{L}(x,y)=f(x)+\Phi(x,y)-h(y)$ with a general coupling term $\Phi(x,y)$ that is not assumed to be bilinear. Given a saddle point $(x^*,y^*)$, assuming $\nabla_y\Phi(\cdot,\cdot)$ is Lipschitz and $\nabla_x\Phi(\cdot,y)$ is Lipschitz in $x$ for any fixed $y$, we…

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