Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Iterates of the Frank-Wolfe Algorithm May Not Converge   The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex
function $f$ over a compact convex set $\mathcal{C}$. While many convergence
results have been derived in terms of function values, hardly nothing is known
about the convergence behavior of the sequence of iterates
$(x_t)_{t\in\mathbb{N}}$. Under the usual assumptions, we design several
counterexamples to the convergence of $(x_t)_{t\in\mathbb{N}}$, where $f$ is
$d$-time continuously differentiable, $d\geq2$, and
$f(x_t)\to\min_\mathcal{C}f$. Our counterexamples cover the cases of open-loop,
closed-loop, and line-search step-size strategies. We do not assume
\emph{misspecification} of the linear minimization oracle and our results thus
hold regardless of the points it returns, demonstrating the fundamental
pathologies in the convergence behavior of $(x_t)_{t\in\mathbb{N}}$.

5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph