相关论文: Separable convex optimization over indegree polyto…

This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…

Many recent applications in machine learning and data fitting call for the algorithmic solution of structured smooth convex optimization problems. Although the gradient descent method is a natural choice for this task, it requires exact…

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi…

Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not…

In this article we study convex integer maximization problems with composite objective functions of the form $f(Wx)$, where $f$ is a convex function on $\R^d$ and $W$ is a $d\times n$ matrix with small or binary entries, over finite sets…

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations.…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…

We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where each of the functions $f(x)$ and $g(y)$ is either affine…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

We study differentially private (DP) optimization algorithms for stochastic and empirical objectives which are neither smooth nor convex, and propose methods that return a Goldstein-stationary point with sample complexity bounds that…

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…