FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3000550340> ?p ?o ?g. }

• W3000550340 endingPage "27" @default.
• W3000550340 startingPage "1" @default.
• W3000550340 abstract "Abstract The limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) method is widely used for large-scale unconstrained optimization, but its behavior on nonsmooth problems has received little attention. L-BFGS (limited memory BFGS) can be used with or without ‘scaling’; the use of scaling is normally recommended. A simple special case, when just one BFGS update is stored and used at every iteration, is sometimes also known as memoryless BFGS. We analyze memoryless BFGS with scaling, using any Armijo–Wolfe line search, on the function $f(x) = a|x^{(1)}| + sum _{i=2}^{n} x^{(i)}$, initiated at any point $x_0$ with $x_0^{(1)}not = 0$. We show that if $age 2sqrt{n-1}$, the absolute value of the normalized search direction generated by this method converges to a constant vector, and if, in addition, $a$ is larger than a quantity that depends on the Armijo parameter, then the iterates converge to a nonoptimal point $bar x$ with $bar x^{(1)}=0$, although $f$ is unbounded below. As we showed in previous work, the gradient method with any Armijo–Wolfe line search also fails on the same function if $ageq sqrt{n-1}$ and $a$ is larger than another quantity depending on the Armijo parameter, but scaled memoryless BFGS fails under a weaker condition relating $a$ to the Armijo parameter than that implying failure of the gradient method. Furthermore, in sharp contrast to the gradient method, if a specific standard Armijo–Wolfe bracketing line search is used, scaled memoryless BFGS fails when $age 2 sqrt{n-1}$regardless of the Armijo parameter. Finally, numerical experiments indicate that the results may extend to scaled L-BFGS with any fixed number of updates $m$, and to more general piecewise linear functions." @default.
• W3000550340 created "2020-01-23" @default.
• W3000550340 creator A5066199970 @default.
• W3000550340 creator A5069099932 @default.
• W3000550340 date "2020-01-18" @default.
• W3000550340 modified "2023-10-17" @default.
• W3000550340 title "Analysis of limited-memory BFGS on a class of nonsmooth convex functions" @default.
• W3000550340 cites W1551360398 @default.
• W3000550340 cites W1993671884 @default.
• W3000550340 cites W1998045815 @default.
• W3000550340 cites W1998749910 @default.
• W3000550340 cites W2051434435 @default.
• W3000550340 cites W2092087339 @default.
• W3000550340 cites W2151568819 @default.
• W3000550340 cites W2484247699 @default.
• W3000550340 cites W2801405307 @default.
• W3000550340 doi "https://doi.org/10.1093/imanum/drz052" @default.
• W3000550340 hasPublicationYear "2020" @default.
• W3000550340 type Work @default.
• W3000550340 sameAs 3000550340 @default.
• W3000550340 citedByCount "5" @default.
• W3000550340 countsByYear W30005503402021 @default.
• W3000550340 countsByYear W30005503402022 @default.
• W3000550340 countsByYear W30005503402023 @default.
• W3000550340 crossrefType "journal-article" @default.
• W3000550340 hasAuthorship W3000550340A5066199970 @default.
• W3000550340 hasAuthorship W3000550340A5069099932 @default.
• W3000550340 hasBestOaLocation W30005503401 @default.
• W3000550340 hasConcept C111472728 @default.
• W3000550340 hasConcept C114614502 @default.
• W3000550340 hasConcept C114954040 @default.
• W3000550340 hasConcept C121332964 @default.
• W3000550340 hasConcept C126255220 @default.
• W3000550340 hasConcept C132721684 @default.
• W3000550340 hasConcept C134306372 @default.
• W3000550340 hasConcept C138885662 @default.
• W3000550340 hasConcept C14036430 @default.
• W3000550340 hasConcept C140479938 @default.
• W3000550340 hasConcept C151319957 @default.
• W3000550340 hasConcept C158622935 @default.
• W3000550340 hasConcept C178635117 @default.
• W3000550340 hasConcept C199360897 @default.
• W3000550340 hasConcept C2524010 @default.
• W3000550340 hasConcept C2777027219 @default.
• W3000550340 hasConcept C2780586882 @default.
• W3000550340 hasConcept C28826006 @default.
• W3000550340 hasConcept C31258907 @default.
• W3000550340 hasConcept C33923547 @default.
• W3000550340 hasConcept C38652104 @default.
• W3000550340 hasConcept C41008148 @default.
• W3000550340 hasConcept C62520636 @default.
• W3000550340 hasConcept C78458016 @default.
• W3000550340 hasConcept C85189116 @default.
• W3000550340 hasConcept C85522705 @default.
• W3000550340 hasConcept C86803240 @default.
• W3000550340 hasConcept C99844830 @default.
• W3000550340 hasConceptScore W3000550340C111472728 @default.
• W3000550340 hasConceptScore W3000550340C114614502 @default.
• W3000550340 hasConceptScore W3000550340C114954040 @default.
• W3000550340 hasConceptScore W3000550340C121332964 @default.
• W3000550340 hasConceptScore W3000550340C126255220 @default.
• W3000550340 hasConceptScore W3000550340C132721684 @default.
• W3000550340 hasConceptScore W3000550340C134306372 @default.
• W3000550340 hasConceptScore W3000550340C138885662 @default.
• W3000550340 hasConceptScore W3000550340C14036430 @default.
• W3000550340 hasConceptScore W3000550340C140479938 @default.
• W3000550340 hasConceptScore W3000550340C151319957 @default.
• W3000550340 hasConceptScore W3000550340C158622935 @default.
• W3000550340 hasConceptScore W3000550340C178635117 @default.
• W3000550340 hasConceptScore W3000550340C199360897 @default.
• W3000550340 hasConceptScore W3000550340C2524010 @default.
• W3000550340 hasConceptScore W3000550340C2777027219 @default.
• W3000550340 hasConceptScore W3000550340C2780586882 @default.
• W3000550340 hasConceptScore W3000550340C28826006 @default.
• W3000550340 hasConceptScore W3000550340C31258907 @default.
• W3000550340 hasConceptScore W3000550340C33923547 @default.
• W3000550340 hasConceptScore W3000550340C38652104 @default.
• W3000550340 hasConceptScore W3000550340C41008148 @default.
• W3000550340 hasConceptScore W3000550340C62520636 @default.
• W3000550340 hasConceptScore W3000550340C78458016 @default.
• W3000550340 hasConceptScore W3000550340C85189116 @default.
• W3000550340 hasConceptScore W3000550340C85522705 @default.
• W3000550340 hasConceptScore W3000550340C86803240 @default.
• W3000550340 hasConceptScore W3000550340C99844830 @default.
• W3000550340 hasFunder F4320306076 @default.
• W3000550340 hasFunder F4320306164 @default.
• W3000550340 hasIssue "1" @default.
• W3000550340 hasLocation W30005503401 @default.
• W3000550340 hasLocation W30005503402 @default.
• W3000550340 hasOpenAccess W3000550340 @default.
• W3000550340 hasPrimaryLocation W30005503401 @default.
• W3000550340 hasRelatedWork W1970748391 @default.
• W3000550340 hasRelatedWork W2356101382 @default.
• W3000550340 hasRelatedWork W2615612939 @default.
• W3000550340 hasRelatedWork W2768763952 @default.
• W3000550340 hasRelatedWork W3139627051 @default.
• W3000550340 hasRelatedWork W4287644333 @default.
• W3000550340 hasRelatedWork W4293559771 @default.

• next