DeepAI AI Chat
Log In Sign Up

Complexity of Linear Minimization and Projection on Some Sets

01/25/2021
by   Cyrille W. Combettes, et al.
0

The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational advantage of solving linear minimizations instead of projections. However, the discussions supporting this advantage are often too succinct or incomplete. In this paper, we review the complexity bounds for both tasks on several sets commonly used in optimization. Projection methods onto the ℓ_p-ball, p∈]1,2[∪]2,+∞[, and the Birkhoff polytope are also proposed.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/18/2019

Inexact Primal-Dual Gradient Projection Methods for Nonlinear Optimization on Convex Set

In this paper, we propose a novel primal-dual inexact gradient projectio...
11/10/2021

Efficient Projection-Free Online Convex Optimization with Membership Oracle

In constrained convex optimization, existing methods based on the ellips...
05/09/2019

Projections onto the canonical simplex with additional linear inequalities

We consider projections onto the canonical simplex with additional linea...
11/22/2022

Projection-free Adaptive Regret with Membership Oracles

In the framework of online convex optimization, most iterative algorithm...
06/29/2020

Shape from Projections via Differentiable Forward Projector

In tomography, forward projection of 3D meshes has been mostly studied t...
09/29/2020

Projection-Free Adaptive Gradients for Large-Scale Optimization

The complexity in large-scale optimization can lie in both handling the ...
11/07/2019

Optimal Projections in the Distance-Based Statistical Methods

This paper introduces a new way to calculate distance-based statistics, ...

Code Repositories

complexity

Complexity of Linear Minimization and Projection on Some Sets


view repo