Research map / Optimization / Nonconvex and smooth optimization
A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Smoothing plus homotopy (smoothing parameter beta_k decreasing as beta0/sqrt(k+1)) within conditional gradient framework for composite problems | composite convex minimization (Algorithm 2) · theoretical convergence | objective residual convergence rate | Helped |
| Use proximal operator of non-smooth term g instead of its subgradient in CGM | non-smooth minimization example (Nesterov counterexample) · counterexample with max{x(1),x(2)} over unit ball | convergence to solution | Helped |
| Inexact linear oracle with additive error of order delta*eta_k (decreasing with k) | Algorithm 2 with approximate LMO · theoretical convergence | objective residual convergence rate | No clear effect |
| Inexact linear oracle with multiplicative error (delta in (0,1]) | Algorithm 2 with approximate LMO · theoretical convergence | objective residual convergence rate | No clear effect |
| Use l1 (least absolute deviations) loss instead of l2 loss in robust PCA / matrix completion inpainting (ablation) | image inpainting with nuclear norm ball and box constraints · 493x517 noisy image, 1000 iterations | PSNR (dB): +5.0 dB (26.0336 vs 21.0496) | Helped |
| Use l1 loss instead of l2 loss in image inpainting (ablation) | image inpainting with nuclear norm ball and box constraints · 493x517 noisy image, 1000 iterations | SSIM: +0.27 (0.80205 vs 0.53145) | Helped |
| Stop early at around 1000 iterations rather than converge fully on MNIST clustering SDP | CGM framework on MNIST clustering · MNIST first 1000 test points | misclassification rate: 0.0914 vs 0.0971 reported for relax-and-round | Helped |
| Replace the classical CGM with the proposed framework on problems with indicator-function non-smooth terms (feasibility-gap guarantees) | SDP and affine-inclusion constrained problems · theoretical convergence | feasibility gap dist(Ax,K) convergence | Helped |
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