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arXiv · 2006.01719

Spectral Frank-Wolfe Algorithm: Strict Complementarity and Linear Convergence

Lijun Ding·Yingjie Fei·Qiantong Xu·Chengrun Yang
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Abstract

We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors of the gradient and solves a small-scale SDP in each iteration. Such procedure overcomes slow convergence of the classical Frank-Wolfe algorithm due to ignoring eigenvalue coalescence. We demonstrate that strict complementarity of the optimization problem is key to proving linear convergence of various algorithms, such as the spectral Frank-Wolfe algorithm as well as the projected gradient method and its accelerated version.

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Lijun Ding, Yingjie Fei, Qiantong Xu, Chengrun Yang. 2020-06-02. Spectral Frank-Wolfe Algorithm: Strict Complementarity and Linear Convergence. https://arxiv.org/abs/2006.01719

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