Related papers: Solving Variational Inequalities with Monotone Ope…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
We consider minimization of composite functions of the form $f(g(x))+h(x)$, where $f$ and $h$ are convex functions (which can be nonsmooth) and $g$ is a smooth vector mapping. In addition, we assume that $g$ is the average of finite number…
Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…
We consider a non-convex constrained optimization problem, where the objective function is weakly convex and the constraint function is either convex or weakly convex. To solve this problem, we consider the classical switching subgradient…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
First-order methods for minimization and saddle point (min-max) problems are widely used for solving large-scale problems, in particular arising in machine learning. The majority of works obtain favorable complexity guarantees of such…
We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
A major approach to saddle point optimization $\min_x\max_y f(x, y)$ is a gradient based approach as is popularized by generative adversarial networks (GANs). In contrast, we analyze an alternative approach relying only on an oracle that…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point…
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…
In a previous work we developed a convex infinite dimensional linear programming (LP) approach to approximating the region of attraction (ROA) of polynomial dynamical systems subject to compact basic semialgebraic state constraints. Finite…
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…