Related papers: A Distributed Continuous-time Modified Newton-Raph…
In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…
Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton's method from which it inherits its fast local quadratic rate. However, unlike Newton's…
This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the…
This paper considers distributed nonconvex optimization with the cost functions being distributed over agents. Noting that information compression is a key tool to reduce the heavy communication load for distributed algorithms as agents…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…