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1.3 Rotated hyper-ellipsoid function Contents1.5 Rastrigin's function 6

1 Parametric Optimization


1.4 Rosenbrock's valley (De Jong's function 2)

Rosenbrock's valley is a classic optimization problem, also known as Banana function. The global optimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial, however convergence to the global optimum is difficult and hence this problem has been repeatedly used in assess the performance of optimization algorithms.

function definition
f2(x)=sum(100·(x(i+1)-x(i)^2)^2+(1-x(i))^2), i=1:n-1;
-2.048<=x(i)<=2.048
.

global minimum
f(x)=0; x(i)=1, i=1:n.

This function is implemented in objfun2.

The first graphic displays the full definition range of the function. The graphic on the right side focuses around the area of the global optimum at [1, 1].
Rosenbrock's valley (De Jong's function 2) Rosenbrock's valley (De Jong's function 2), local


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