אלגוריתמי פראנק-ולף מסוגלים: תנאי תלות וצפיפות

תקציר מקורי באנגליתarXiv:2511.02821v2 Announce Type: replace-cross Abstract: We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given by the spectrahedron and nuclear-norm balls. A key technical ingredient is a complementarity condition that captures solution sparsity---face dimension for polytopes and rank for matrices. We present two algorithms: (1) a purely linear optimization oracle (LOO) method for polytopes that has optimal worst-case first-order (FO) oracle complexity and, aside of a finite \emph{burn-in} phase and up to a logarithmic factor, has LOO complexity that scales with $r/\sqrt{\epsilon}$, where $\epsilon$ is the