Stability has been a recurrent issue in training generative adversarial networks (GANs). One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods specifically designed for this adversarial training. In this work, we review the “variational inequality” framework which contains most formulation...

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal O(1/k) rate of convergence. Compared to the optimal non-SP algorithms, our...

In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k -Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter cont...

In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a selfconcordant barrier and whose underlying map has Lipschitz continuous derivative. In contrast to the method of [7] in which each iteration required an approximate solution of a linearized variational inequality over ...

This paper describes a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. It is shown that the pointwise iteration-complexity of the new method is better than the corresponding one for the standard ADMM method and that, up to a logarithmic term, is identical to the ergodic iteration-complexity of the latter method. Our...

In this paper, we consider block-decomposition first-order methods for solving large-scale conic semidefinite programming problems given in standard form. Several ingredients are introduced to speedup the method in its pure form such as: an aggressive choice of stepsize for performing the extragradient step; use of scaled inner products; dynamic update of the scaled inner product for properly b...