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This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
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…