相关论文: Extracting Dual Solutions via Primal Optimizers

We investigate different aspects of area convexity [Sherman '17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with more…

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in…

An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…

Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational…

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…

By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…

Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…

Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…

We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…

Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a regularized surrogate with algorithms based on simple…