Related papers: Inexact and Stochastic Generalized Conditional Gra…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…

This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as…

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…

In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…

This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…

We consider the misspecified optimization problem of minimizing a convex function $f(x;\theta^*)$ in $x$ over a conic constraint set represented by $h(x;\theta^*) \in \mathcal{K}$, where $\theta^*$ is an unknown (or misspecified) vector of…

The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been re-developed for minimizing convex composite problems without the global Lipschitz gradient…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…

This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…