Related papers: Relative Lipschitzness in Extragradient Methods an…
In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…
We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most $O(1/\epsilon)$…
In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
We introduce prox-convex for minimizing $F(x)=g(x)+h(C(x))+s(R(x))$, where $g$ and $h$ are convex, $C$ and $s$ are smooth, and each component of $R$ is convex (possibly nonsmooth). Here $g$ captures general convex objectives and indicator…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global $O(1/\sqrt{T})$ convergence rate for any convex function…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
The usual approach to developing and analyzing first-order methods for non-smooth (stochastic or deterministic) convex optimization assumes that the objective function is uniformly Lipschitz continuous with parameter $M_f$. However, in many…
Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…