Related papers: On the convergence analysis of DCA

Stochastic differentiable approximation schemes are widely used for solving high dimensional problems. Most of existing methods satisfy some desirable properties, including conditional descent inequalities, and almost sure (a.s.)…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

This paper concerns a class of constrained difference-of-convex (DC) optimization problems in which, the constraint functions are continuously differentiable and their gradients are strictly continuous. For such nonconvex and nonsmooth…

Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

We propose a new approach to perform the boosted difference of convex functions algorithm (BDCA) on non-smooth and non-convex problems involving the difference of convex (DC) functions. The recently proposed BDCA uses an extrapolation step…

Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training. However, theoretical…

In this work and its accompanying Part II [1], we develop an accelerated algorithmic framework, DAMA (Decentralized Accelerated Minimax Approach), for nonconvex Polyak-Lojasiewicz minimax optimization over decentralized multi-agent…

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…

It is proved that, for an indefinite quadratic programming problem under linear constraints, any iterative sequence generated by the Proximal DC decomposition algorithm $R$-linearly converges to a Karush-Kuhn-Tucker point, provided that the…

Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice…

With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known…

In this paper, we consider a class of single-ratio fractional minimization problems, where both the numerator and denominator of the objective are convex functions satisfying positive homogeneity. Many nonsmooth optimization problems on the…

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC…

Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of…

In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the…

In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…

Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…

This paper proposes a novel Difference-of-Convex (DC) decomposition for polynomials using a power-sum representation, achieved by solving a sparse linear system. We introduce the Boosted DCA with Exact Line Search (BDCAe) for addressing…