Broyden–Fletcher–Goldfarb–Shanno algorithm
optimization method
| rdfs:label |
"Broyden–Fletcher–Goldfarb–Shanno algorithm"@en
|
|
skos:alt |
"BFGS algorithm"@en
|
| schema:description |
"optimization method"@en
|
|
schema:date |
"2026-02-28T23:32:41+00:00"^^xsd:dateTime |
| schema:version | 2468157286 |
| wikibase:identifiers | 4 |
| wikibase:sitelinks | 9 |
| wikibase:statements | 18 |
| p:P10283 | wd:statement/Q2877013-CC53E777-00CB-47A3-9C86-3AF7DD281E6A |
| p:P138 | wd:statement/Q2877013-5dfa6864-41d1-20ec-f00d-e5c573c4764d |
| wd:statement/Q2877013-efb02450-42da-89f8-f3ab-cdb2ff1382a8 | |
| wd:statement/Q2877013-f498e4b6-47cd-57df-df4f-e802384fc025 | |
| wd:statement/Q2877013-ffddccfa-4209-34f3-2c55-b42884dd1eff | |
| p:P2159 | wd:statement/Q2877013-4f952cf4-4971-046f-5eb4-0fdc9fc4e6dd |
| p:P2534 | wd:statement/Q2877013-3c2599ad-434e-b8dd-eab1-8b8eb71df3e7 |
| p:P2581 | wd:statement/Q2877013-09F0EF84-471D-4E54-ABB3-3A2E538622C7 |
| p:P279 | wd:statement/Q2877013-38e4f622-44d1-9eb2-025e-e373879596cf |
| p:P31 | wd:statement/Q2877013-6656505f-4e2a-a880-49a8-81c6a6fa7fbf |
| p:P361 | wd:statement/Q2877013-d1429693-48dd-561e-d9af-23b38fad8138 |
| p:P61 | wd:statement/Q2877013-69611cfc-4695-857e-a0ae-6ca29f2a5a3f |
| wd:statement/Q2877013-a654515e-42b8-650a-31f0-31f246e21206 | |
| wd:statement/Q2877013-c14728fd-4a6d-ec1a-753a-30267706f3c9 | |
| wd:statement/Q2877013-c70603a5-445a-3548-34d0-da667a87acfa | |
| p:P6104 | wd:statement/Q2877013-E042984F-AB28-46A8-AC85-B1DBFCC335BA |
| p:P6366 | wd:statement/Q2877013-5F64893E-E6F4-47AE-AD12-015C0E107ADD |
| p:P646 | wd:statement/Q2877013-BB969830-81B1-4AE0-A3DA-1820C87FBD76 |
|
p:direct- |
<http:/ |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C132721684" |
| wdt:P138 | David Shanno |
| Donald Goldfarb | |
| Charles George Broyden | |
| Roger Fletcher | |
| wdt:P2159 | optimization problem |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><msub><mi>𝐩</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mtd><mtd><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msubsup><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msubsup><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><msub><mi>𝐟</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mtd><mtd><mo stretchy="false">=</mo><mi>arg</mi><mo>⁡</mo><mi>min</mi><mo>⁡</mo><mi>f</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><msub><mi>𝐱</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub><mo mathvariant="bold" stretchy="false">+</mo><mi mathvariant="bold-italic">α</mi><mrow data-mjx-texclass="ORD"><msub><mi>𝐩</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub><mo stretchy="false" mathvariant="bold">)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><msub><mi>𝐬</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mtd><mtd><mo stretchy="false">=</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mrow data-mjx-texclass="ORD"><msub><mi>𝐩</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><msub><mi>𝐱</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝐤</mi><mo mathvariant="bold" stretchy="false">+</mo><mn>𝟏</mn></mrow></mrow></msub></mrow></mtd><mtd><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><msub><mi>𝐱</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub><mo mathvariant="bold" stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><msub><mi>𝐬</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><msub><mi>𝐲</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝐤</mi><mo mathvariant="bold" stretchy="false">+</mo><mn>𝟏</mn></mrow></mrow></msub></mrow></mtd><mtd><mo stretchy="false">=</mo><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><msub><mi>𝐟</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝐤</mi><mo mathvariant="bold" stretchy="false">+</mo><mn>𝟏</mn></mrow></mrow></msub><mo mathvariant="bold" stretchy="false">−</mo><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><msub><mi>𝐟</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mrow></mtd></mtr><mtr><mtd><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msub></mtd><mtd><mo stretchy="false">=</mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>𝐲</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub><mrow data-mjx-texclass="ORD"><msubsup><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">⊤</mi></mrow></msubsup></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msubsup><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">⊤</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><msub><mi>𝐬</mi><mrow data-mjx-texclass="ORD"><mi>𝐤</mi></mrow></msub></mrow></mrow></mrow></mfrac></mrow><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mi>𝐬</mi></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msubsup><mrow data-mjx-texclass="ORD"><mi>𝐬</mi></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">⊤</mi></mrow></msubsup><msubsup><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">⊤</mi></mrow></msubsup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msubsup><mrow data-mjx-texclass="ORD"><mi>𝐬</mi></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">⊤</mi></mrow></msubsup><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mi>𝐬</mi></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2581 | "17280119n" |
| wdt:P279 | Quasi-Newton method |
| wdt:P31 | algorithm |
| wdt:P361 | nonlinear programming |
| wdt:P61 | David Shanno |
| Donald Goldfarb | |
| Charles George Broyden | |
| Roger Fletcher | |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "132721684" |
| wdt:P646 | "/m/066pcg" |
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