Related papers: Fast Projection Onto Convex Smooth Constraints

In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…

This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\triangle^n$. Utilizing the Moreau's identity, we show that the problem is essentially a univariate minimization and the objective…

Using sparse-inducing norms to learn robust models has received increasing attention from many fields for its attractive properties. Projection-based methods have been widely applied to learning tasks constrained by such norms. As a key…

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

In this paper, a new variant of accelerated gradient descent is proposed. The pro-posed method does not require any information about the objective function, usesexact line search for the practical accelerations of convergence, converges…

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…

Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper proposes projected primal-dual dynamical system approaches…

In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…

This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project…

In this paper, we deal with the problem of optimizing a black-box smooth function over a full-dimensional smooth convex set. We study sets of feasible curves that allow to properly characterize stationarity of a solution and possibly carry…

We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…

We consider solving large scale nonconvex optimisation problems with nonnegativity constraints. Such problems arise frequently in machine learning, such as nonnegative least-squares, nonnegative matrix factorisation, as well as problems…

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…