Related papers: Popov Mirror-Prox for solving Variational Inequali…
We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…
Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…
In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative…
It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…