相关论文: A Bregman forward-backward linesearch algorithm fo…

This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive…

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…

We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form $f(\mathbf{u})+\tau_1 \|\mathbf{u}\|_1 + \tau_2 \|D\,\mathbf{u}\|_1$, where $f$ is a smooth convex function and $D$…

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…

This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…

In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…

Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…

In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent iterative method, is proposed and analyzed to find multiple…

In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…

We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…

Blind deconvolution is a technique to recover an original signal without knowing a convolving filter. It is naturally formulated as a minimization of a quartic objective function under some assumption. Because its differentiable part does…

Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…

We propose an innovative algorithm for non-convex composite federated learning that decouples the proximal operator evaluation and the communication between server and clients. Moreover, each client uses local updates to communicate less…

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…

We prove that the block-coordinate Frank-Wolfe (BCFW) algorithm converges with state-of-the-art rates in both convex and nonconvex settings under a very mild "block-iterative" assumption. This appears to be the first result on BCFW…

The linearized Bregman iterations (LBreI) and its variants are powerful tools for finding sparse or low-rank solutions to underdetermined linear systems. In this study, we propose a cut-and-project perspective for the linearized Bregman…

In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for…

Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…

Optimization problems involving the minimization of a finite sum of smooth, possibly non-convex functions arise in numerous applications. To achieve a consensus solution over a network, distributed optimization algorithms, such as…