Geodesic
Short Paper - A note on the Frank–Wolfe algorithm for a class of nonconvex and nonsmooth optimization problems
de Oliveira, Welington1
1 Mines Paris, Université PSL, Centre de Mathématiques Appliquées (CMA), 06904 Sophia Antipolis, France
Open Journal of Mathematical Optimization, Tome 4 (2023), article no. 2, 10 p.

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Frank and Wolfe’s celebrated conditional gradient method is a well-known tool for solving smooth optimization problems for which minimizing a linear function over the feasible set is computationally cheap. However, when the objective function is nonsmooth, the method may fail to compute a stationary point. In this work, we show that the Frank–Wolfe algorithm can be employed to compute Clarke-stationary points for nonconvex and nonsmooth optimization problems consisting of minimizing upper-C 1,α functions over convex and compact sets. Furthermore, under more restrictive assumptions, we propose a new algorithm variant with stronger stationarity guarantees, namely directional stationarity and even local optimality.

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DOI : 10.5802/ojmo.21
Keywords: Nonsmooth Optimization, Nonconvex Optimization, Frank–Wolfe Algorithm

de Oliveira, Welington 1

1 Mines Paris, Université PSL, Centre de Mathématiques Appliquées (CMA), 06904 Sophia Antipolis, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Short {Paper} - {A} note on the {Frank{\textendash}Wolfe} algorithm for a class of nonconvex and nonsmooth optimization problems},
     journal = {Open Journal of Mathematical Optimization},
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de Oliveira, Welington. Short Paper - A note on the Frank–Wolfe algorithm for a class of nonconvex and nonsmooth optimization problems. Open Journal of Mathematical Optimization, Tome 4 (2023), article  no. 2, 10 p.. doi: 10.5802/ojmo.21

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