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 BD2412 9 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]