# Dual Prices for Frank--Wolfe Algorithms

arXiv: https://arxiv.org/abs/2101.02087 · HTML: https://mlsanity.com/paper/2101.02087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [Convex mixed-integer optimization with Frank-Wolfe methods](https://mlsanity.com/paper/2208.11010/) (2022)

## Abstract (arXiv)

In this note we observe that for constrained convex minimization problems minx ∈ Pf(x) over a polytope P, dual prices for the linear program minz ∈ P nabla f(x) z obtained from linearization at approximately optimal solutions x have a similar interpretation of rate of change in optimal value as for linear programming, providing a convex form of sensitivity analysis. This is of particular interest for Frank--Wolfe algorithms (also called conditional gradients), forming an important class of first-order methods, where a basic building block is linear minimization of gradients of f over P, which in most implementations already compute the dual prices as a by-product.