Related papers: A Primal-Dual Quasi-Newton Method for Exact Consen…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

Stochastic optimization methods have become a class of popular optimization tools in machine learning. Especially, stochastic gradient descent (SGD) has been widely used for machine learning problems such as training neural networks due to…

We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent…

In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other…

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…

In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type…

Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…

Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Decentralized primal-dual methods are widely used for solving decentralized optimization problems, but their updates often rely on the potentially crude first-order Taylor approximations of the objective functions, which can limit…

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…

In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In…

In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…

In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…

In this paper, we propose the first Quasi-Newton method with a global convergence rate of $O(k^{-1})$ for general convex functions. Quasi-Newton methods, such as BFGS, SR-1, are well-known for their impressive practical performance.…

In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…