Research map / Optimization / Nonconvex and smooth optimization
Self-Concordant Analysis of Frank-Wolfe Algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the adaptive self-concordant step size V1 | Frank-Wolfe · General self-concordant optimization | function-value convergence rate: O(1/k) | Helped |
| Use backtracking with a local Lipschitz estimate (V2) | Frank-Wolfe · General self-concordant optimization | function-value convergence rate: O(k^{-1}) | Helped |
| Add an LLOO and the proposed adaptive step sizes | Frank-Wolfe · Self-concordant optimization over polytopes | function-value convergence rate: h_{k}\leq \gap(x^{0})\exp\left(-\frac{1}{2}\sum_{i=0}^{k-1}\alpha_{i}\right) | Helped |
| Use proximal Newton instead of a Frank-Wolfe-based method | Methods compared in the experiments · Poisson inverse problem and portfolio optimization | relative error | Helped |
| Use Variant 2 | Frank-Wolfe · Portfolio optimization | computation time | Helped |
| Use Variant 2 | Frank-Wolfe · Poisson inverse problem, higher relative-error targets | computation time | Helped |
| Choose among the tested Frank-Wolfe step-size policies | Frank-Wolfe · Poisson inverse problem and portfolio optimization | relative error | No clear effect |
| Use the LLOO-based method rather than the standard step size | Frank-Wolfe · Portfolio optimization | iteration complexity | No clear effect |
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