Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298203201> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W4298203201 abstract "The problem of minimizing an objective that can be written as the sum of a set of $n$ smooth and strongly convex functions is considered. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and incremental methods that have a cost per iteration independent of $n$. IQN iterations are a stochastic version of BFGS iterations that use memory to reduce the variance of stochastic approximations. The convergence properties of IQN bridge a gap between deterministic and stochastic quasi-Newton methods. Deterministic quasi-Newton methods exploit the possibility of approximating the Newton step using objective gradient differences. They are appealing because they have a smaller computational cost per iteration relative to Newton's method and achieve a superlinear convergence rate under customary regularity assumptions. Stochastic quasi-Newton methods utilize stochastic gradient differences in lieu of actual gradient differences. This makes their computational cost per iteration independent of the number of objective functions $n$. However, existing stochastic quasi-Newton methods have sublinear or linear convergence at best. IQN is the first stochastic quasi-Newton method proven to converge superlinearly in a local neighborhood of the optimal solution. IQN differs from state-of-the-art incremental quasi-Newton methods in three aspects: (i) The use of aggregated information of variables, gradients, and quasi-Newton Hessian approximation matrices to reduce the noise of gradient and Hessian approximations. (ii) The approximation of each individual function by its Taylor's expansion in which the linear and quadratic terms are evaluated with respect to the same iterate. (iii) The use of a cyclic scheme to update the functions in lieu of a random selection routine. We use these fundamental properties of IQN to establish its local superlinear convergence rate." @default.
- W4298203201 created "2022-10-01" @default.
- W4298203201 creator A5008417632 @default.
- W4298203201 creator A5078862959 @default.
- W4298203201 creator A5091474691 @default.
- W4298203201 date "2017-02-02" @default.
- W4298203201 modified "2023-10-16" @default.
- W4298203201 title "IQN: An Incremental Quasi-Newton Method with Local Superlinear Convergence Rate" @default.
- W4298203201 doi "https://doi.org/10.48550/arxiv.1702.00709" @default.
- W4298203201 hasPublicationYear "2017" @default.
- W4298203201 type Work @default.
- W4298203201 citedByCount "0" @default.
- W4298203201 crossrefType "posted-content" @default.
- W4298203201 hasAuthorship W4298203201A5008417632 @default.
- W4298203201 hasAuthorship W4298203201A5078862959 @default.
- W4298203201 hasAuthorship W4298203201A5091474691 @default.
- W4298203201 hasBestOaLocation W42982032011 @default.
- W4298203201 hasConcept C112680207 @default.
- W4298203201 hasConcept C114954040 @default.
- W4298203201 hasConcept C117160843 @default.
- W4298203201 hasConcept C117898588 @default.
- W4298203201 hasConcept C121332964 @default.
- W4298203201 hasConcept C126255220 @default.
- W4298203201 hasConcept C127162648 @default.
- W4298203201 hasConcept C134306372 @default.
- W4298203201 hasConcept C145446738 @default.
- W4298203201 hasConcept C158622935 @default.
- W4298203201 hasConcept C159694833 @default.
- W4298203201 hasConcept C162324750 @default.
- W4298203201 hasConcept C179127668 @default.
- W4298203201 hasConcept C203616005 @default.
- W4298203201 hasConcept C2524010 @default.
- W4298203201 hasConcept C26517878 @default.
- W4298203201 hasConcept C2777303404 @default.
- W4298203201 hasConcept C28826006 @default.
- W4298203201 hasConcept C31258907 @default.
- W4298203201 hasConcept C33923547 @default.
- W4298203201 hasConcept C38652104 @default.
- W4298203201 hasConcept C41008148 @default.
- W4298203201 hasConcept C50522688 @default.
- W4298203201 hasConcept C55479107 @default.
- W4298203201 hasConcept C57869625 @default.
- W4298203201 hasConcept C62520636 @default.
- W4298203201 hasConcept C85189116 @default.
- W4298203201 hasConceptScore W4298203201C112680207 @default.
- W4298203201 hasConceptScore W4298203201C114954040 @default.
- W4298203201 hasConceptScore W4298203201C117160843 @default.
- W4298203201 hasConceptScore W4298203201C117898588 @default.
- W4298203201 hasConceptScore W4298203201C121332964 @default.
- W4298203201 hasConceptScore W4298203201C126255220 @default.
- W4298203201 hasConceptScore W4298203201C127162648 @default.
- W4298203201 hasConceptScore W4298203201C134306372 @default.
- W4298203201 hasConceptScore W4298203201C145446738 @default.
- W4298203201 hasConceptScore W4298203201C158622935 @default.
- W4298203201 hasConceptScore W4298203201C159694833 @default.
- W4298203201 hasConceptScore W4298203201C162324750 @default.
- W4298203201 hasConceptScore W4298203201C179127668 @default.
- W4298203201 hasConceptScore W4298203201C203616005 @default.
- W4298203201 hasConceptScore W4298203201C2524010 @default.
- W4298203201 hasConceptScore W4298203201C26517878 @default.
- W4298203201 hasConceptScore W4298203201C2777303404 @default.
- W4298203201 hasConceptScore W4298203201C28826006 @default.
- W4298203201 hasConceptScore W4298203201C31258907 @default.
- W4298203201 hasConceptScore W4298203201C33923547 @default.
- W4298203201 hasConceptScore W4298203201C38652104 @default.
- W4298203201 hasConceptScore W4298203201C41008148 @default.
- W4298203201 hasConceptScore W4298203201C50522688 @default.
- W4298203201 hasConceptScore W4298203201C55479107 @default.
- W4298203201 hasConceptScore W4298203201C57869625 @default.
- W4298203201 hasConceptScore W4298203201C62520636 @default.
- W4298203201 hasConceptScore W4298203201C85189116 @default.
- W4298203201 hasLocation W42982032011 @default.
- W4298203201 hasLocation W42982032012 @default.
- W4298203201 hasOpenAccess W4298203201 @default.
- W4298203201 hasPrimaryLocation W42982032011 @default.
- W4298203201 hasRelatedWork W2587483164 @default.
- W4298203201 hasRelatedWork W2964248513 @default.
- W4298203201 hasRelatedWork W3001734434 @default.
- W4298203201 hasRelatedWork W3130457203 @default.
- W4298203201 hasRelatedWork W3167047574 @default.
- W4298203201 hasRelatedWork W3206532668 @default.
- W4298203201 hasRelatedWork W4289537470 @default.
- W4298203201 hasRelatedWork W4298203201 @default.
- W4298203201 hasRelatedWork W4320558430 @default.
- W4298203201 hasRelatedWork W914658793 @default.
- W4298203201 isParatext "false" @default.
- W4298203201 isRetracted "false" @default.
- W4298203201 workType "article" @default.