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A first-order augmented Lagrangian method for constrained minimax optimization
In this paper we study a class of constrained minimax problems.
First-order penalty methods for bilevel optimization
Under suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$ and $O(\varepsilon^{-7}\log\varepsilon^{-1})$, measured by their fundamental operations, is established for the proposed penalty methods for finding an $\varepsilon$-KKT solution of the unconstrained and constrained bilevel optimization problems, respectively.
Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuity with applications to variational inequality, conic constrained saddle point, and convex conic optimization problems
In particular, we first propose a primal-dual extrapolation (PDE) method for solving a structured strongly MI problem by modifying the classical forward-backward splitting method by using a point and operator extrapolation technique, in which the parameters are adaptively updated by a backtracking line search scheme.
Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient
In particular, we first consider unconstrained convex optimization with LLCG and propose accelerated proximal gradient (APG) methods for solving it.
