相关论文: Minimizing smooth Kurdyka-{\L}ojasiewicz functions…
We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this…
This paper deals with nonconvex optimization problems via a two-level smoothing framework in which the high-order Moreau envelope (HOME) is applied to generate a smooth approximation of weakly convex cost functions. As such, the…
Conventional wisdom in composite optimization suggests augmented Lagrangian dual ascent (ALDA) in Peaceman-Rachford splitting (PRS) methods for dual feasibility. However, ALDA may fail when the primal iterate is a local minimum, a…
This paper is devoted to a detailed convergence analysis of the method of codifferential descent (MCD) developed by professor V.F. Demyanov for solving a large class of nonsmooth nonconvex optimization problems. We propose a generalization…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
In this paper, we consider a class of generalized difference-of-convex functions (DC) programming, whose objective is the difference of two convex (not necessarily smooth) functions plus a decomposable (possibly nonconvex) function with…
In this paper we analyze a family of general random block coordinate descent methods for the minimization of $\ell_0$ regularized optimization problems, i.e. the objective function is composed of a smooth convex function and the $\ell_0$…
There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…
The application of a zeroth-order scheme for minimising Polyak-\L{}ojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global…
This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…
Coordinate descent algorithms are popular for huge-scale optimization problems due to their low cost per-iteration. Coordinate descent methods apply to problems where the constraint set is separable across coordinates. In this paper, we…
The Boosted Difference of Convex functions Algorithm (BDCA) was recently proposed for minimizing smooth difference of convex (DC) functions. BDCA accelerates the convergence of the classical Difference of Convex functions Algorithm (DCA)…
This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Gradient descent ascent (GDA), the simplest single-loop algorithm for nonconvex minimax optimization, is widely used in practical applications such as generative adversarial networks (GANs) and adversarial training. Albeit its desirable…
The analysis of projection-free first order methods is often complicated by the presence of different kinds of "good" and "bad" steps. In this article, we propose a unifying framework for projection-free methods, aiming to simplify the…
We study first order methods to compute the barycenter of a probability distribution $P$ over the space of probability measures with finite second moment. We develop a framework to derive global rates of convergence for both gradient…