Draft:Beale Function

Submission declined on 16 May 2023 by Raydann (talk).

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This draft has not been edited in over six months and qualifies to be deleted per CSD G13.

Declined by Raydann 23 months ago. Last edited by Raydann 23 months ago. Reviewer: Inform author.

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In mathematical optimization, Beale function is a multi-modal function, used to test the performance of optimization algorithms.^[1] The function is defined by:

$f(x,y)=(1.5-x+xy)^{2}+(2.25-x+xy^{2})^{2}+(2.625-x+xy^{3})^{3}$ with $(x,y)\in \mathbb {R} ^{2}$

The Beale function is typically constrained to the subset $-5\leq x,y\leq 5$ and admits a unique global minimum at $f(3,0.5)=0$

References

^ Alvarez, F.; Cabot, A. (Feb 2004). "Steepest Descent with Curvature Dynamical System". Journal of Optimization Theory and Applications. 120 (2): 270–271. doi:10.1023/B:JOTA.0000015684.50827.49. ISSN 0022-3239. S2CID 122310173.

[1] Alvarez, F.; Cabot, A. (Feb 2004). "Steepest Descent with Curvature Dynamical System". Journal of Optimization Theory and Applications. 120 (2): 270–271. doi:10.1023/B:JOTA.0000015684.50827.49. ISSN 0022-3239. S2CID 122310173.

[1]