Matches in SemOpenAlex for { <https://semopenalex.org/work/W1992386684> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W1992386684 endingPage "111" @default.
- W1992386684 startingPage "84" @default.
- W1992386684 abstract "Ill-conditioning has long been regarded as a plague on interior methods, but its damaging effects have rarely been documented. In fact, implementors of interior methods who ignore warnings about the dire consequences of ill-conditioning usually manage to compute accurate solutions. We offer some insight into this seeming contradiction by analyzing ill-conditioning within a primal-dual method in which the full, usually well-conditioned primal-dual matrix is transformed to a condensed, inherently ill-conditioned matrix Mpd . We show that ill-conditioning in the exact condensed matrix closely resembles that known for the primal barrier Hessian, and then examine the influence of cancellation in the computed constraints. Using the structure of Mpd , various bounds are obtained on the absolute accuracy of the computed primal-dual steps. Without cancellation, the portion of the computed x step in the small space of Mpd (a subspace close to the null space of the Jacobian of the active constraints) has an absolute error bound comparable to machine precision, and its large-space component has a much smaller error bound. With cancellation (the usual case), the absolute error bounds for both the small- and large-space components of the computed x step are comparable to machine precision. In either case, the absolute error bound for the computed multiplier steps associated with active constraints is comparable to machine precision; the computed multiplier steps for inactive constraints, although converging to zero, retain (approximately) full relative precision. Because of errors in forming the right-hand side, the absolute error in the computed solution of the full, well-conditioned primal-dual system is shown to be comparable to machine precision. Thus, under quite general conditions, ill-conditioning in Mpd does not noticeably impair the accuracy of the computed primal-dual steps. (A similar analysis applies to search directions obtained by direct solution of the primal Newton equations.)" @default.
- W1992386684 created "2016-06-24" @default.
- W1992386684 creator A5009900911 @default.
- W1992386684 date "1998-01-01" @default.
- W1992386684 modified "2023-09-29" @default.
- W1992386684 title "Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming" @default.
- W1992386684 cites W1967810262 @default.
- W1992386684 cites W1978554456 @default.
- W1992386684 cites W1984633545 @default.
- W1992386684 cites W1989242344 @default.
- W1992386684 cites W1991682620 @default.
- W1992386684 cites W1992386684 @default.
- W1992386684 cites W2010223115 @default.
- W1992386684 cites W2017666390 @default.
- W1992386684 cites W2036622774 @default.
- W1992386684 cites W2046222402 @default.
- W1992386684 cites W2049973411 @default.
- W1992386684 cites W2053627399 @default.
- W1992386684 cites W2066668812 @default.
- W1992386684 cites W2071425572 @default.
- W1992386684 cites W2072175279 @default.
- W1992386684 cites W2083431695 @default.
- W1992386684 cites W2092677228 @default.
- W1992386684 cites W2094435468 @default.
- W1992386684 cites W2134847890 @default.
- W1992386684 cites W2140997052 @default.
- W1992386684 doi "https://doi.org/10.1137/s1052623497322279" @default.
- W1992386684 hasPublicationYear "1998" @default.
- W1992386684 type Work @default.
- W1992386684 sameAs 1992386684 @default.
- W1992386684 citedByCount "86" @default.
- W1992386684 countsByYear W19923866842012 @default.
- W1992386684 countsByYear W19923866842013 @default.
- W1992386684 countsByYear W19923866842014 @default.
- W1992386684 countsByYear W19923866842015 @default.
- W1992386684 countsByYear W19923866842016 @default.
- W1992386684 countsByYear W19923866842017 @default.
- W1992386684 countsByYear W19923866842018 @default.
- W1992386684 countsByYear W19923866842019 @default.
- W1992386684 countsByYear W19923866842021 @default.
- W1992386684 countsByYear W19923866842023 @default.
- W1992386684 crossrefType "journal-article" @default.
- W1992386684 hasAuthorship W1992386684A5009900911 @default.
- W1992386684 hasConcept C106487976 @default.
- W1992386684 hasConcept C11413529 @default.
- W1992386684 hasConcept C121332964 @default.
- W1992386684 hasConcept C122383733 @default.
- W1992386684 hasConcept C126255220 @default.
- W1992386684 hasConcept C134306372 @default.
- W1992386684 hasConcept C158693339 @default.
- W1992386684 hasConcept C159985019 @default.
- W1992386684 hasConcept C192562407 @default.
- W1992386684 hasConcept C203616005 @default.
- W1992386684 hasConcept C28826006 @default.
- W1992386684 hasConcept C32834561 @default.
- W1992386684 hasConcept C33923547 @default.
- W1992386684 hasConcept C62520636 @default.
- W1992386684 hasConcept C84545080 @default.
- W1992386684 hasConceptScore W1992386684C106487976 @default.
- W1992386684 hasConceptScore W1992386684C11413529 @default.
- W1992386684 hasConceptScore W1992386684C121332964 @default.
- W1992386684 hasConceptScore W1992386684C122383733 @default.
- W1992386684 hasConceptScore W1992386684C126255220 @default.
- W1992386684 hasConceptScore W1992386684C134306372 @default.
- W1992386684 hasConceptScore W1992386684C158693339 @default.
- W1992386684 hasConceptScore W1992386684C159985019 @default.
- W1992386684 hasConceptScore W1992386684C192562407 @default.
- W1992386684 hasConceptScore W1992386684C203616005 @default.
- W1992386684 hasConceptScore W1992386684C28826006 @default.
- W1992386684 hasConceptScore W1992386684C32834561 @default.
- W1992386684 hasConceptScore W1992386684C33923547 @default.
- W1992386684 hasConceptScore W1992386684C62520636 @default.
- W1992386684 hasConceptScore W1992386684C84545080 @default.
- W1992386684 hasIssue "1" @default.
- W1992386684 hasLocation W19923866841 @default.
- W1992386684 hasOpenAccess W1992386684 @default.
- W1992386684 hasPrimaryLocation W19923866841 @default.
- W1992386684 hasRelatedWork W2018064504 @default.
- W1992386684 hasRelatedWork W2086619942 @default.
- W1992386684 hasRelatedWork W2209797896 @default.
- W1992386684 hasRelatedWork W2401062588 @default.
- W1992386684 hasRelatedWork W2589711910 @default.
- W1992386684 hasRelatedWork W2963461064 @default.
- W1992386684 hasRelatedWork W3004956525 @default.
- W1992386684 hasRelatedWork W4306743306 @default.
- W1992386684 hasRelatedWork W4308012852 @default.
- W1992386684 hasRelatedWork W4313532632 @default.
- W1992386684 hasVolume "9" @default.
- W1992386684 isParatext "false" @default.
- W1992386684 isRetracted "false" @default.
- W1992386684 magId "1992386684" @default.
- W1992386684 workType "article" @default.