Related papers: Strongly Convex Optimization for Joint Fractal Fea…

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

Texture is intuitively defined as a repeated arrangement of a basic pattern or object in an image. There is no mathematical definition of a texture though. The human visual system is able to identify and segment different textures in a…

The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

We develop a novel gradient-based algorithm for optimizing nonsmooth nonconvex functions where nonsmoothness arises from explicit nonsmooth operators in the objective's analytical form. Our key innovation involves encoding active smooth…

We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the…

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…

In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…

We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…

We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute),…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…