Matches in SemOpenAlex for { <https://semopenalex.org/work/W3129078050> ?p ?o ?g. }
- W3129078050 abstract "We study a class of convex-concave saddle-point problems of the form $min_xmax_y langle Kx,yrangle+f_{cal{P}}(x)-h^ast(y)$ where $K$ is a linear operator, $f_{cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope $cal{P}$, and $h^ast$ is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle ($lmo$) for $f_{cal{P}}$ and an efficient proximal map for $h^*$ which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case $h^*$ is the indicator function of a linear constraint and function $f$ is quadratic, we show a $O(1/n^2)$ convergence rate on the dual objective, requiring $O(n log n)$ calls of $lmo$. If the problem comes from the constrained optimization problem $min_{xinmathbb R^d}{f_{cal{P}}(x):|:Ax-b=0}$ then we additionally get bound $O(1/n^2)$ both on the primal gap and on the infeasibility gap. In the most general case, we show a $O(1/n)$ convergence rate of the primal-dual gap again requiring $O(nlog n)$ calls of $lmo$. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems. We show applications to labeling problems frequently appearing in machine learning and computer vision." @default.
- W3129078050 created "2021-02-15" @default.
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- W3129078050 date "2021-01-29" @default.
- W3129078050 modified "2023-09-27" @default.
- W3129078050 title "One-sided Frank-Wolfe algorithms for saddle problems" @default.
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