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In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to guarantee the optimal iteration complexity bound of $mathcal{O}left(kappaln(1/epsilon)right)$ to reach an $epsilon$-solution, where $kappa$ is the condition number. This framework provides the flexibility for algorithm designers to train -- among different parameter combinations -- the one that best suits the structure of the problem class at hand. The proposed framework includes the following iterative points and directions as its constituents: the extra-gradient, the optimistic gradient descent ascent (OGDA) direction (aka optimism), the heavy-ball direction, and Nesterovs extrapolation points. As a result, all the afore-mentioned methods become the special cases under the general scheme of extra points. We also specialize this approach to strongly convex minimization, and show that a similar extra-point approach achieves the optimal iteration complexity bound of $mathcal{O}(sqrt{kappa}ln(1/epsilon))$ for this class of problems.
In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a general sch
We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the $p^{th}$-order derivatives are Lipschitz continuous, we give an al
We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the optimization va
The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on monotone or
In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing approximate stron