Related papers: Beyond the Golden Ratio for Variational Inequality…
In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…
In this work, we solve a 49-year open problem, the general optimal step-size for ADMM-type algorithms. For a convex program: $\text{min.} \,\, f({x}) + g({z})$, $\text{s.t.}\, {A}{x} - {B}{z} = {c} $, given an arbitrary fixed-point…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…
We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…
Surprisingly, recent work has shown that gradient descent can be accelerated without using momentum -- just by judiciously choosing stepsizes. An open question raised by several papers is whether this phenomenon of stepsize-based…
Golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow-Hurwicz method for solving structured convex optimization problem, in which the objective function consists of the sum of two closed proper convex functions,…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a zeroth-order…
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,…
The monotone variational inequality is a central problem in mathematical programming that unifies and generalizes many important settings such as smooth convex optimization, two-player zero-sum games, convex-concave saddle point problems,…
We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax…
In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with…
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…
Motivated by problems arising in decentralized control problems and non-cooperative Nash games, we consider a class of strongly monotone Cartesian variational inequality (VI) problems, where the mappings either contain expectations or their…