Optimisation Visualisation
Numerical optimisation algorithms are found in almost every industry and application. However, grasping these algorithms can be tricky for beginners and non-expert users. We therefore present a visual aid for common optimisation algorithms on several common test functions.
Sphere Function
Classic quadratic function
$$f(x,y) = x^2 + y^2$$
$$(x^*,y^*) = (0,0)$$
Test It Out!
2D Rastrigin Function
Multimodal, continuous, non-convex
$$f(x,y) = 20 + \sum_{i=1}^{2} x_i^2 - 10 \cos(2\pi x_i)$$
$$(x^*,y^*) = (0,0)$$
Test It Out!
2D Rosenbrock Function
Unimodal, continuous, non-convex
$$f(x,y) = (a-x)^2 + b(y-x^2)^2$$
$$(x^*,y^*) = (1,1)$$
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Beale Function
Multimodal, continuous, non-convex
$$f(x,y) = (1.5-x+xy)^2 + (2.25-x+xy^2)^2 + (2.625-x+xy^3)^2$$
$$(x^*,y^*) = (3,0.5)$$
Test It Out!