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Frank-wolfe algorithm for star-convex functions
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DOI：10.1007/s11590-026-02307-8.png)
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Abstract
En 中文
We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical com-plexity bounds to certain non-convex functions, we focus on the class of star-con-vex functions, which retain essential geometric properties despite the lack of con-vexity. We establish iteration-complexity bounds of O(1/k) for both the objective values and the duality gap under star-convexity, using diminishing, Armijo-type, and Lipschitz-based stepsize rules. Notably, the diminishing and Armijo strategies do not require prior knowledge of Lipschitz or curvature constants. These results demonstrate that the Frank-Wolfe method preserves optimal complexity guarantees beyond the convex setting.
Keywords:
Frank-Wolfe method
Star-convex functions
Non-convex function
Journal
O
IF:
1.1
Papers:
72
Citations:
2.4K