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Conditional Gradient Methods
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The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.
Forward citations
Cited by 10 Pith papers
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Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise
Lion and Muon with weight decay are shown to be instances of one stochastic Frank-Wolfe algorithm, and clipped and variance-reduced variants get the first high-probability convergence rates for nonconvex Frank-Wolfe u...
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Secant Line Search for Frank-Wolfe Algorithms
A secant-method line search computes near-exact Frank-Wolfe step sizes in few gradient evaluations, claiming to match exact line search in theory and practice.
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Computing Approximate Graph Edit Distance via Optimal Transport
Deriving the node-matching matrix from a cost matrix via optimal transport improves approximate graph edit distance and edit path generation on small benchmark graphs.
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A Frank-Wolfe Algorithm for Oracle-based Robust Optimization
A smoothed Frank-Wolfe algorithm solves oracle-based robust optimization with 4 D^2 M^2 / eps^2 oracle calls and gives the first explicit oracle-call bound for min-max-min robust optimization.
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An Absolute-Error Proximal Bundle Method through the Lens of Frank-Wolf
A modified proximal bundle method with a fixed absolute accuracy null-step test is shown via Frank-Wolfe duality to have O(ε^{-4/5} log^{2/5}(1/ε)) iteration complexity.
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Minimum enclosing Bregman balls made easy
Left Bregman MEBs equal power MEBs on dual Laguerre points; Frank-Wolfe power approximation recovers the 2005 Bregman algorithm, and Bregman liftings equal paraboloid liftings.
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A Unified Toolbox for Multipartite Entanglement Certification
Conditional gradient methods can certify multipartite entanglement heuristically and rigorously, with improved noise robustness bounds for Horodecki states.
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A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization
A Frank-Wolfe method that adapts both the smoothness constant and the triangle-scaling exponent achieves sublinear convergence and a tolerance-dependent linear rate, with a centralized distributed optimization application.
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Observing High-dimensional Bell Inequality Violations using Multi-Outcome Spectral Measurements
Measuring only the joint spectral intensity of a time-bin entangled two-photon state suffices to violate the CGLMP Bell inequality up to dimension 8 using genuinely multi-outcome measurements.
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Efficient Sparse Flow Decomposition Methods for RNA Multi-Assembly
Sparse flow decomposition is reformulated as a convex fit over the flow polytope and solved with Frank-Wolfe, yielding fast, competitive reconstructions that do not require explicit path-count minimization.
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