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We present a unified viewpoint of proximal point method (PPM), primal-dual hybrid gradient (PDHG) and alternating direction method of multipliers (ADMM) for solving convex-concave primal-dual problems. This viewpoint shows the equivalence…

This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…

We propose a computer-assisted approach to the analysis of the worst-case convergence of nonlinear conjugate gradient methods (NCGMs). Those methods are known for their generally good empirical performances for large-scale optimization,…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is…

We consider a nonsmooth optimization problem on Riemannian manifold, whose objective function is the sum of a differentiable component and a nonsmooth convex function. We propose a manifold inexact augmented Lagrangian method (MIALM) for…

In this paper, we analyze the convergence of Alternating Direction Method of Multipliers (ADMM) on convex quadratic programs (QPs) with linear equality and bound constraints. The ADMM formulation alternates between an equality constrained…

In this paper we will review recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier--free stabilised methods. We first show how the method generates Galerkin/Least…

We consider the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under the Kurdyka-Lojasiewicz assumption, we prove that the sequence produced by the extragradient method…

The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations on surfaces. The solvers are built on top of the well-known…

We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…

In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on…

We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is…

We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order…

This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization…

In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…

We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can…

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme…

Inexact proximal augmented Lagrangian methods (ipALMs) have been widely used for solving linearly constrained convex optimization problems, owing to their strong theoretical guarantees and excellent numerical performance. In practice,…

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…