## SLiSeS: Subsampled Line Search Spectral Gradient Method for Finite Sums

Citation SLiSes Article Download View SLiSeS: Subsampled Line Search Spectral Gradient Method for Finite Sums

Citation SLiSes Article Download View SLiSeS: Subsampled Line Search Spectral Gradient Method for Finite Sums

Article Download View AN-SPS: Adaptive Sample Size Nonmonotone Line Search Spectral Projected Subgradient Method for Convex Constrained Optimization Problems

We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual (local) strongly convex costs. Alternating Direction Method of Multipliers (ADMM) and Proximal Method of Multipliers (PMM) have been proved to be effective frameworks for design of exact distributed second order methods … Read more

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves … Read more

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at … Read more

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using Inexact Restoration-based adapted sample sizes. The sample size is chosen in an adaptive manner based on Inexact Restoration. The algorithm uses line search … Read more

We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation – transforming the original problem into a constrained problem in a higher dimensional space – to define a sequence of suitable quadratic penalty subproblems with increasing penalty … Read more

This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton step and global convergence is enforced by a nonmonotone line search procedure. The aim is to obtain methods with affordable costs and fast … Read more

We consider unconstrained minimization of a finite sum of $N$ continuously differentiable, not necessarily convex, cost functions. Several gradient-like (and more generally, line search) methods, where the full gradient (the sum of $N$ component costs’ gradients) at each iteration~$k$ is replaced with an inexpensive approximation based on a sub-sample~$\mathcal N_k$ of the component costs’ gradients, … Read more

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 attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second-order information … Read more