Research map / Optimization / Nonconvex and smooth optimization
Convergence guarantees for a class of non-convex and non-smooth optimization problems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the double-loop CCCP updates with the proposed single-loop proximal-type method | Best subset selection · Synthetic data, across tested dimensions and sparsity levels | runtime | Helped |
| Replace CCCP with the proposed proximal-type method | Best subset selection · Synthetic data, low sparsity | estimation error | No clear effect |
| Replace CCCP with the proposed proximal-type method | Best subset selection · Synthetic data, moderate to large sparsity | estimation error | Helped |
| Use a KL-structured objective rather than a general objective | Gradient-type and proximal-type algorithms · Bounded sequences satisfying the KL inequality | gradient norm convergence rate: at least 1/k; general non-convex rate is \order(1/\sqrt{k}) | Helped |
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