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Function used as a performance test problem for optimization algorithms
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can be found analytically. However, because they are roots of
179:{\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\quad }
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is a multi-modal function, used to test the performance of
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430:{\displaystyle f(-3.779310,-3.283186)=0.0,\quad }
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476:{\displaystyle f(3.584428,-1.848126)=0.0.\quad }
378:{\displaystyle f(-2.805118,3.131312)=0.0,\quad }
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329:{\displaystyle f(3.0,2.0)=0.0,\quad }
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288:, and four identical local minima:
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501:(1924–2011), who introduced it.
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622:Test functions for optimization
511:Test functions for optimization
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68:. The function is defined by:
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281:{\displaystyle f(x,y)=181.617}
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532:Applied Nonlinear Programming
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575:. You can help Knowledge by
497:The function is named after
189:It has one local maximum at
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627:Mathematical analysis stubs
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240:{\displaystyle y=-0.923039}
211:{\displaystyle x=-0.270845}
49:Log-spaced level curve plot
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486:The locations of all the
58:mathematical optimization
499:David Mautner Himmelblau
530:Himmelblau, D. (1972).
66:optimization algorithms
571:–related article is a
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569:mathematical analysis
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62:Himmelblau's function
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577:expanding it
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616:Categories
517:References
458:−
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505:See also
461:1.848126
452:3.584428
412:3.283186
403:3.779310
360:3.131312
354:2.805118
235:0.923039
206:0.270845
276:181.617
538:
488:minima
247:where
567:This
35:In 3D
573:stub
536:ISBN
470:0.0.
218:and
421:0.0
369:0.0
320:0.0
311:2.0
305:3.0
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