相关论文: Block Alternating Bregman Majorization Minimizatio…

We introduce some new proximal quasi-Newton methods for unconstrained multiobjective optimization problems (in short, UMOP), where each objective function is the sum of a twice continuously differentiable strongly convex function and a…

We introduce a unified algorithmic framework, called proximal-like incremental aggregated gradient (PLIAG) method, for minimizing the sum of a convex function that consists of additive relatively smooth convex components and a proper lower…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

Cyclic block coordinate methods are a fundamental class of optimization methods widely used in practice and implemented as part of standard software packages for statistical learning. Nevertheless, their convergence is generally not well…

We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the…

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

In this paper, for solving a broad class of large-scale nonconvex and nonsmooth optimization problems, we propose a stochastic two step inertial Bregman proximal alternating linearized minimization (STiBPALM) algorithm with variance-reduced…

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 $D$…

Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this paper, we propose the Bregman parallel direction method of…

In this work, we develop a level-set subdifferential error bound condition aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It…

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its…

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}\Phi(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling…

Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models.…

We introduce a new algorithm for complex image reconstruction with separate regularization of the image magnitude and phase. This optimization problem is interesting in many different image reconstruction contexts, although is nonconvex and…

Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms…

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…

In this paper we study the auxiliary problems that appear in $p$-order tensor methods for unconstrained minimization of convex functions with $\nu$-H\"{o}lder continuous $p$th derivatives. This type of auxiliary problems corresponds to the…

Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past…

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…