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! Name !! Plot !! Formula !! Global minimum !! Search ___domain
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| Rosenbrock function constrained with a cubic and a line<ref>{{cite conference |author1=Simionescu, P.A. |author2=Beale, D. |title=New Concepts in Graphic Visualization of Objective Functions |conference=ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |___location=Montreal, Canada |date=September 29 – October 2, 2002|pages=891–897 |url=http://faculty.tamucc.edu/psimionescu/PDFs/DETC02-DAC-34129.pdf |access-date=7 January 2017 }}</ref>
|| [[File:Rosenbrock cubic constraint.svg|200px|Rosenbrock function constrained with a cubic and a line]]
|| <math>f(x,y) = (1-x)^2 + 100(y-x^2)^2</math>,
subjected to: <math> (x-1)^3 - y + 1 \le 0 \text{ and } x + y - 2 \le 0 </math>
|| <math>f(1.0,1.0) = 0</math>
|| <math>-1.5\le x \le 1.5</math>, <math>-0.5\le y \le 2.5</math>
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| Rosenbrock function constrained to a disk<ref>{{Cite web|url=https://www.mathworks.com/help/optim/ug/example-nonlinear-constrained-minimization.html?requestedDomain=www.mathworks.com|title=Solve a Constrained Nonlinear Problem - MATLAB & Simulink|website=www.mathworks.com|access-date=2017-08-29}}</ref>
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|| <math>f(2.0052938,1.1944509) = -2.0239884</math>
|| <math>-2.25\le x \le 2.25</math>, <math>-2.5\le y \le 1.75</math>
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| Gomez and Levy function (modified)<ref>{{cite journal |last1=Simionescu |first1=P.A. |date=2020 |title=A collection of bivariate nonlinear optimisation test problems with graphical representations |url= |journal=International Journal of Mathematical Modelling and Numerical Optimisation |volume=10 |issue=4 |pages=365–398 |doi=10.1504/IJMMNO.2020.110704 |access-date=}}</ref>
|| [[File:Gomez-Levi contour.svg|200px|Gomez and Levy Function]]
|| <math>f(x,y) = 4 x^2 - 2.1 x^4 + \frac 1 3 x^6 + xy - 4y^2 +4 y^4 </math>,
subjected to:<math> -\sin(4 \pi x) + 2\sin^2(2 \pi y) \le 1.5 </math>
|| <math>f(0.08984201,-0.7126564) = -1.031628453</math>
|| <math>-1\le x \le 0.75</math>, <math>-1\le y \le 1</math>
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| [[Simionescu function]]<ref>{{cite book|last=Simionescu|first=P.A.|title=Computer Aided Graphing and Simulation Tools for AutoCAD Users|year=2014|publisher=CRC Press|___location=Boca Raton, FL|isbn=978-1-4822-5290-3|edition=1st}}</ref>
|| [[File:Simionescu contour.svg|200px|Simionescu function]]
|| <math>f(x,y) = 0.1xy</math>,
subjected to: <math> x^2+y^2\le\left[r_{T}+r_{S}\cos\left(n \arctan \frac{x}{y} \right)\right]^2</math>
<math>\text{where: } r_{T}=1, r_{S}=0.2 \text{ and } n = 8</math>
|| <math>f(\pm 0.84852813,\mp 0.84852813) = -0.072</math>
|| <math>-1.25\le x,y \le 1.25</math>
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| Gomez and Levy function (modified)<ref>{{cite journal |last1=Simionescu |first1=P.A. |date=2020 |title=A collection of bivariate nonlinear optimisation test problems with graphical representations |url= |journal=International Journal of Mathematical Modelling and Numerical Optimisation |volume=10 |issue=4 |pages=365–398 |doi=10.1504/IJMMNO.2020.110704 |access-date=}}</ref>
|| [[File:Gomez-Levi contour.svg|200px|Gomez and Levy Function]]
|| <math>f(x,y) = 4 x^2 - 2.1 x^4 + \frac 1 3 x^6 + xy - 4y^2 +4 y^4 </math>,
subjected to:<math> -\sin(4 \pi x) + 2\sin^2(2 \pi y) \le 1.5 </math>
|| <math>f(0.08984201,-0.7126564) = -1.031628453</math>
|| <math>-1\le x \le 0.75</math>, <math>-1\le y \le 1</math>
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