Matches in SemOpenAlex for { <https://semopenalex.org/work/W2072994709> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2072994709 endingPage "1684" @default.
- W2072994709 startingPage "1655" @default.
- W2072994709 abstract "We present a new “lifting” approach for the solution of nonlinear optimization problems (NLPs) that have objective and constraint functions with intermediate variables. Introducing these as additional degrees of freedom into the original problem, combined with adding suitable new constraints to ensure equivalence of the problems, we propose to solve this augmented system instead of the original system by a Newton-type method. This often offers advantages in terms of convergence rates and region of attraction. The main contribution of this article is an efficient algorithmic trick to generate the quantities needed for a Newton-type method on the augmented (“lifted”) system with (a) almost no additional computational cost per iteration compared to a nonlifted Newton method, and (b) with negligible programming burden. We derive lifted schemes for Newton's method, as well as for constrained Gauss–Newton and adjoint based sequential quadratic programming (SQP) methods, and show equivalence of the new efficiently lifted approaches with “full-space” lifted Newton iterations. We establish conditions on the intermediate functions that imply faster local quadratic convergence for lifted versus nonlifted Newton iterations, a phenomenon often observed in practice but not yet explained theoretically. Finally, we compare numerically the behavior of the lifted approach with the nonlifted approach on several test problems, including a large scale example with 27 million intermediate variables. The algorithms and examples are available as open-source code in the C++ package LiftOpt." @default.
- W2072994709 created "2016-06-24" @default.
- W2072994709 creator A5034083794 @default.
- W2072994709 creator A5057375078 @default.
- W2072994709 date "2010-01-01" @default.
- W2072994709 modified "2023-10-02" @default.
- W2072994709 title "The Lifted Newton Method and Its Application in Optimization" @default.
- W2072994709 cites W1964031104 @default.
- W2072994709 cites W1983864916 @default.
- W2072994709 cites W1994309501 @default.
- W2072994709 cites W2000062047 @default.
- W2072994709 cites W2061606863 @default.
- W2072994709 cites W2077008103 @default.
- W2072994709 cites W4233170985 @default.
- W2072994709 cites W4234298991 @default.
- W2072994709 doi "https://doi.org/10.1137/080724885" @default.
- W2072994709 hasPublicationYear "2010" @default.
- W2072994709 type Work @default.
- W2072994709 sameAs 2072994709 @default.
- W2072994709 citedByCount "68" @default.
- W2072994709 countsByYear W20729947092012 @default.
- W2072994709 countsByYear W20729947092013 @default.
- W2072994709 countsByYear W20729947092014 @default.
- W2072994709 countsByYear W20729947092015 @default.
- W2072994709 countsByYear W20729947092016 @default.
- W2072994709 countsByYear W20729947092017 @default.
- W2072994709 countsByYear W20729947092018 @default.
- W2072994709 countsByYear W20729947092019 @default.
- W2072994709 countsByYear W20729947092020 @default.
- W2072994709 countsByYear W20729947092021 @default.
- W2072994709 countsByYear W20729947092022 @default.
- W2072994709 countsByYear W20729947092023 @default.
- W2072994709 crossrefType "journal-article" @default.
- W2072994709 hasAuthorship W2072994709A5034083794 @default.
- W2072994709 hasAuthorship W2072994709A5057375078 @default.
- W2072994709 hasConcept C115527620 @default.
- W2072994709 hasConcept C117898588 @default.
- W2072994709 hasConcept C118615104 @default.
- W2072994709 hasConcept C121332964 @default.
- W2072994709 hasConcept C126255220 @default.
- W2072994709 hasConcept C158622935 @default.
- W2072994709 hasConcept C159694833 @default.
- W2072994709 hasConcept C162324750 @default.
- W2072994709 hasConcept C178635117 @default.
- W2072994709 hasConcept C179127668 @default.
- W2072994709 hasConcept C198927703 @default.
- W2072994709 hasConcept C2777303404 @default.
- W2072994709 hasConcept C2780069185 @default.
- W2072994709 hasConcept C28826006 @default.
- W2072994709 hasConcept C33923547 @default.
- W2072994709 hasConcept C38652104 @default.
- W2072994709 hasConcept C41008148 @default.
- W2072994709 hasConcept C50522688 @default.
- W2072994709 hasConcept C62520636 @default.
- W2072994709 hasConcept C81845259 @default.
- W2072994709 hasConcept C85189116 @default.
- W2072994709 hasConcept C89109886 @default.
- W2072994709 hasConceptScore W2072994709C115527620 @default.
- W2072994709 hasConceptScore W2072994709C117898588 @default.
- W2072994709 hasConceptScore W2072994709C118615104 @default.
- W2072994709 hasConceptScore W2072994709C121332964 @default.
- W2072994709 hasConceptScore W2072994709C126255220 @default.
- W2072994709 hasConceptScore W2072994709C158622935 @default.
- W2072994709 hasConceptScore W2072994709C159694833 @default.
- W2072994709 hasConceptScore W2072994709C162324750 @default.
- W2072994709 hasConceptScore W2072994709C178635117 @default.
- W2072994709 hasConceptScore W2072994709C179127668 @default.
- W2072994709 hasConceptScore W2072994709C198927703 @default.
- W2072994709 hasConceptScore W2072994709C2777303404 @default.
- W2072994709 hasConceptScore W2072994709C2780069185 @default.
- W2072994709 hasConceptScore W2072994709C28826006 @default.
- W2072994709 hasConceptScore W2072994709C33923547 @default.
- W2072994709 hasConceptScore W2072994709C38652104 @default.
- W2072994709 hasConceptScore W2072994709C41008148 @default.
- W2072994709 hasConceptScore W2072994709C50522688 @default.
- W2072994709 hasConceptScore W2072994709C62520636 @default.
- W2072994709 hasConceptScore W2072994709C81845259 @default.
- W2072994709 hasConceptScore W2072994709C85189116 @default.
- W2072994709 hasConceptScore W2072994709C89109886 @default.
- W2072994709 hasIssue "3" @default.
- W2072994709 hasLocation W20729947091 @default.
- W2072994709 hasOpenAccess W2072994709 @default.
- W2072994709 hasPrimaryLocation W20729947091 @default.
- W2072994709 hasRelatedWork W1512804140 @default.
- W2072994709 hasRelatedWork W2025795821 @default.
- W2072994709 hasRelatedWork W2044725063 @default.
- W2072994709 hasRelatedWork W2072994709 @default.
- W2072994709 hasRelatedWork W2098918699 @default.
- W2072994709 hasRelatedWork W2167631998 @default.
- W2072994709 hasRelatedWork W2188032279 @default.
- W2072994709 hasRelatedWork W2808820944 @default.
- W2072994709 hasRelatedWork W3023414632 @default.
- W2072994709 hasRelatedWork W574348691 @default.
- W2072994709 hasVolume "20" @default.
- W2072994709 isParatext "false" @default.
- W2072994709 isRetracted "false" @default.
- W2072994709 magId "2072994709" @default.
- W2072994709 workType "article" @default.