Virtual Library of Simulation Experiments:

Optimization Test Problems

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Sum Squares Function

Description:

Dimensions: d

The Sum Squares function, also referred to as the Axis Parallel Hyper-Ellipsoid function, has no local minimum except the global one. It is continuous, convex and unimodal. It is shown here in its two-dimensional form.

Input Domain:

The function is usually evaluated on the hypercube x_i ∈ [-10, 10], for all i = 1, …, d, although this may be restricted to the hypercube x_i ∈ [-5.12, 5.12], for all i = 1, …, d.

Global Minimum:

Code:

References:

Global Optimization Test Problems. Retrieved June 2013, from
http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm.

Molga, M., & Smutnicki, C. Test functions for optimization needs (2005). Retrieved June 2013, from http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf.

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For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.