Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300503045> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W4300503045 abstract "In a Hilbert space, we provide a fast dynamic approach to the hierarchical minimization problem which consists in finding the minimum norm solution of a convex minimization problem. For this, we study the convergence properties of the trajectories generated by a damped inertial dynamic with Tikhonov regularization. When the time goes to infinity, the Tikhonov regularization parameter is supposed to tend towards zero, not too fast, which is a key property to make the trajectories strongly converge towards the minimizer of $f$ of minimum norm. According to the structure of the heavy ball method for strongly convex functions, the viscous damping coefficient is proportional to the square root of the Tikhonov regularization parameter. Therefore, it also converges to zero, which will ensure rapid convergence of values. Precisely, under a proper tuning of these parameters, based on Lyapunov's analysis, we show that the trajectories strongly converge towards the minimizer of minimum norm, and we provide the convergence rate of the values. We show a trade off between the property of fast convergence of values, and the property of strong convergence towards the minimum norm solution. This study improves several previous works where this type of results was obtained under restrictive hypotheses." @default.
- W4300503045 created "2022-10-03" @default.
- W4300503045 creator A5022578878 @default.
- W4300503045 creator A5025093667 @default.
- W4300503045 creator A5025710979 @default.
- W4300503045 creator A5038818485 @default.
- W4300503045 date "2021-07-31" @default.
- W4300503045 modified "2023-10-02" @default.
- W4300503045 title "Damped inertial dynamics with vanishing Tikhonov regularization: strong asymptotic convergence towards the minimum norm solution" @default.
- W4300503045 doi "https://doi.org/10.48550/arxiv.2108.00203" @default.
- W4300503045 hasPublicationYear "2021" @default.
- W4300503045 type Work @default.
- W4300503045 citedByCount "0" @default.
- W4300503045 crossrefType "posted-content" @default.
- W4300503045 hasAuthorship W4300503045A5022578878 @default.
- W4300503045 hasAuthorship W4300503045A5025093667 @default.
- W4300503045 hasAuthorship W4300503045A5025710979 @default.
- W4300503045 hasAuthorship W4300503045A5038818485 @default.
- W4300503045 hasBestOaLocation W43005030451 @default.
- W4300503045 hasConcept C121332964 @default.
- W4300503045 hasConcept C127162648 @default.
- W4300503045 hasConcept C134306372 @default.
- W4300503045 hasConcept C135252773 @default.
- W4300503045 hasConcept C141718189 @default.
- W4300503045 hasConcept C152442038 @default.
- W4300503045 hasConcept C154945302 @default.
- W4300503045 hasConcept C173386949 @default.
- W4300503045 hasConcept C17744445 @default.
- W4300503045 hasConcept C191795146 @default.
- W4300503045 hasConcept C199539241 @default.
- W4300503045 hasConcept C2776135515 @default.
- W4300503045 hasConcept C27872270 @default.
- W4300503045 hasConcept C28826006 @default.
- W4300503045 hasConcept C31258907 @default.
- W4300503045 hasConcept C33923547 @default.
- W4300503045 hasConcept C41008148 @default.
- W4300503045 hasConcept C57869625 @default.
- W4300503045 hasConcept C62520636 @default.
- W4300503045 hasConceptScore W4300503045C121332964 @default.
- W4300503045 hasConceptScore W4300503045C127162648 @default.
- W4300503045 hasConceptScore W4300503045C134306372 @default.
- W4300503045 hasConceptScore W4300503045C135252773 @default.
- W4300503045 hasConceptScore W4300503045C141718189 @default.
- W4300503045 hasConceptScore W4300503045C152442038 @default.
- W4300503045 hasConceptScore W4300503045C154945302 @default.
- W4300503045 hasConceptScore W4300503045C173386949 @default.
- W4300503045 hasConceptScore W4300503045C17744445 @default.
- W4300503045 hasConceptScore W4300503045C191795146 @default.
- W4300503045 hasConceptScore W4300503045C199539241 @default.
- W4300503045 hasConceptScore W4300503045C2776135515 @default.
- W4300503045 hasConceptScore W4300503045C27872270 @default.
- W4300503045 hasConceptScore W4300503045C28826006 @default.
- W4300503045 hasConceptScore W4300503045C31258907 @default.
- W4300503045 hasConceptScore W4300503045C33923547 @default.
- W4300503045 hasConceptScore W4300503045C41008148 @default.
- W4300503045 hasConceptScore W4300503045C57869625 @default.
- W4300503045 hasConceptScore W4300503045C62520636 @default.
- W4300503045 hasLocation W43005030451 @default.
- W4300503045 hasLocation W43005030452 @default.
- W4300503045 hasLocation W43005030453 @default.
- W4300503045 hasOpenAccess W4300503045 @default.
- W4300503045 hasPrimaryLocation W43005030451 @default.
- W4300503045 hasRelatedWork W1966857445 @default.
- W4300503045 hasRelatedWork W1974309151 @default.
- W4300503045 hasRelatedWork W2382338669 @default.
- W4300503045 hasRelatedWork W2947090029 @default.
- W4300503045 hasRelatedWork W2975497547 @default.
- W4300503045 hasRelatedWork W3047953937 @default.
- W4300503045 hasRelatedWork W3090176247 @default.
- W4300503045 hasRelatedWork W4287062219 @default.
- W4300503045 hasRelatedWork W4288346649 @default.
- W4300503045 hasRelatedWork W4300503045 @default.
- W4300503045 isParatext "false" @default.
- W4300503045 isRetracted "false" @default.
- W4300503045 workType "article" @default.