相关论文: An Adaptive Regularized Proximal Newton-Type Metho…

We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…

We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective…

In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…

This work presents a thorough numerical study of Riemannian Newton's Method (RNM) for optimization problems, with a focus on the Grassmannian and on the Stiefel manifold. We compare the Riemannian formulation of Newton's Method with its…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…

This study proposes a cubic regularization of the Newton method for generating weakly efficient points of unconstrained vector optimization problems under no convexity assumption on the objective function. It is observed that at a given…

We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem…

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that…

We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…

We propose LeAP-SSN (Levenberg--Marquardt Adaptive Proximal Semismooth Newton method), a semismooth Newton-type method with a simple, parameter-free globalisation strategy that guarantees convergence from arbitrary starting points in…

In this paper, a class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization on a networked system are developed, where nodes in the networked system seek for a consensus that minimizes the sum of their…

Adaptive regularization with cubics (ARC) is an algorithm for unconstrained, non-convex optimization. Akin to the popular trust-region method, its iterations can be thought of as approximate, safe-guarded Newton steps. For cost functions…

We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches…

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the…