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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…
In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a DC (Difference of Convex functions) function, where the differentiable function is not restricted to the global Lipschitz gradient…
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…
In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…
We consider the problem of minimizing a difference-of-convex (DC) function, which can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous possibly nonsmooth concave…
This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms…
In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…
We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
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…
This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy…
The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation…
Several decades ago the Proximal Point Algorithm (PPA) started to gain a long-lasting attraction for both abstract operator theory and numerical optimization communities. Even in modern applications, researchers still use proximal…
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…
In this paper, we consider a composite difference-of-convex (DC) program, whose objective function is the sum of a smooth convex function with Lipschitz continuous gradient, a proper closed and convex function, and a continuous concave…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
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)…
Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…