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Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank andPhilip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival,fuelled by the need of fast and reliable first-order optimization methods inData Science and other relevant application areas. This review tries to explainthe success of this approach by illustrating versatility and applicability in awide range of contexts, combined with an account on recent progress invariants, both improving on the speed and efficiency of this surprisinglysimple principle of first-order optimization.

Frank-Wolfe and friends: a journey into projection-free first-order optimization methods