Related papers: Linearly contrained nonsmooth and nonconvex minimi…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…
In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
In this paper, we develop two Riemannian stochastic smoothing algorithms for nonsmooth optimization problems on Riemannian manifolds, addressing distinct forms of the nonsmooth term \( h \). Both methods combine dynamic smoothing with a…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…
Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…
We propose a duality scheme for solving constrained nonsmooth and nonconvex optimization problems in a reflexive Banach space. We establish strong duality for a very general type of augmented Lagrangian, in which we assume a less…
In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…