Descending Everest with First-Order Oracles: Oracle Complexity of Convex Optimization under $(L_0,L_1)$-Smoothness DWQANBV7B7
| URI | m2://res/DWQANBV7B7 |
|---|---|
| Kind | preprint |
| Creators | Mikhail Rudomanov, Ivan Fomin, Alexander V. Gasnikov, Fedor S. Stonyakin |
| Date | 2026-10-15 |
| MSC | 49-XX, 90-XX, 93-XX |
| Subjects | arxiv math.OC |
| Scope | in |
Expressions
e1: version, preprint
| Language | en |
|---|---|
| Date | 2026-10-15 |
| Ids | arXiv 2610.21461, zbl_id 903214008 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| Membership in the class | statement | lemma 4.4 | arxiv |
| Upper bounds under a bounded initial optimality gap | statement | theorem B.7 | arxiv |
| Inequality at the minimizer | statement | lemma 3.2 | arxiv |
| Upper bound for the radius-only class | statement | theorem 3.7 | arxiv |
| Orthogonal invariance principle | statement | proposition 4.3 | arxiv |
| Choice of the chain length | statement | lemma 4.9 | arxiv |
| Distance to the minimizer | statement | lemma 4.7 | arxiv |
| Smoothness of the conjugate function | statement | lemma 4.2 | arxiv |
| Inexact line search | statement | lemma 3.3 | arxiv |
| Center-of-gravity method | statement | proposition C.1 | arxiv |
| Counting with a positive initial weight | statement | lemma B.6 | arxiv |
| Characterization of the class | statement | lemma 2.2 | arxiv |
| FFYK9ZSXE6 | statement | lemma 3.4 | arxiv |
| FRY5PSXF0R | statement | lemma 4.6 | arxiv |
| Lower bound for the radius-only class | statement | theorem 4.10 | arxiv |
| Lower bound on the class with bounded initial optimality gap | statement | theorem B.3 | arxiv |
| Properties of the chain with equal slopes | statement | lemma B.1 | arxiv |
| GTWCVC9VM7 | definition | definition 4.1 | arxiv |
| Consequences of Grönwall's inequality | statement | lemma A.1 | arxiv |
| Descent lemma | statement | lemma 3.1 | arxiv |
| MDCPCMGJX2 | statement | lemma B.4 | arxiv |
| Block bound | statement | lemma B.5 | arxiv |
| Class condition for equal slopes | statement | lemma B.2 | arxiv |
| Number of first-stage iterations | statement | lemma 3.5 | arxiv |
| RNDME2KDGS | statement | theorem | arxiv |
| Second stage | statement | proposition 3.6 | arxiv |
| Lower bound for the chain with decreasing slopes | statement | theorem 4.8 | arxiv |
| SWAAB93QNC | statement | lemma 4.5 | arxiv |
| TY8QWTQSGA | definition | definition | arxiv |
| Growth around the minimizer | statement | lemma A.2 | arxiv |
| Function class | definition | definition 2.1 | arxiv |
Catalogue records
- arxiv: 2610.21461 (work)
- arxiv_text: 2610.21461 (work)
- zbmath_search: 903214008 (work)