相关论文: Lipschitz-free Projected Subgradient Method with T…

We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter…

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…

We show that the vanishing stepsize subgradient method -- widely adopted for machine learning applications -- can display rather messy behavior even in the presence of favorable assumptions. We establish that convergence of bounded…

We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel…

We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set,…

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

Prescribed-time convergence mechanism has become a prominent research focus in the current field of optimization and control due to its ability to precisely control the target completion time. The recently arisen prescribed-time algorithms…

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…

It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…

In this paper, we provide a sub-gradient based algorithm to solve general constrained convex optimization without taking projections onto the domain set. The well studied Frank-Wolfe type algorithms also avoid projections. However, they are…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…

Recent works by Altschuler and Parrilo and the authors have shown that it is possible to accelerate the convergence of gradient descent on smooth convex functions, even without momentum, just by picking special stepsizes. In this paper, we…

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed…

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require…

Projected policy gradient (PPG) is a basic policy optimization method in reinforcement learning. Given access to exact policy evaluations, previous studies have established the sublinear convergence of PPG for sufficiently small step sizes…

Efficient computation of min-max problems is a central question in optimization, learning, games, and controls. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued…

Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…

We propose a new stepsize for the gradient method. It is shown that this new stepsize will converge to the reciprocal of the largest eigenvalue of the Hessian, when Dai-Yang's asymptotic optimal gradient method (Computational Optimization…