Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

The Rosenbrock function[32] is a wellknown test problem for optimization algorithms. The standard formulation includes two design variables, and computes a single objective function. This problem can also be posed as a leastsquares optimization problem with two residuals to be minimzed because the objective function is the sum of squared terms.
Standard Formulation
The standard twodimensional formulation can be stated as
Surface and contour plots for this function are shown in the Dakota User's Manual.
The optimal solution is:
with
A LeastSquares Optimization Formulation
This test problem may also be used to exercise leastsquares solution methods by recasting the standard problem formulation into:
are residual terms.
The included analysis driver can handle both formulations. In the Dakota/test
directory, the rosenbrock
executable (compiled from Dakota_Source/test/rosenbrock.cpp
) checks the number of response functions passed in the parameters file and returns either an objective function (as computed from Equation rosenstd) for use with optimization methods or two least squares terms (as computed from Equations rosenr1 rosenr2 ) for use with least squares methods. Both cases support analytic gradients of the function set with respect to the design variables. See the User's Manual for examples of both cases (search for Rosenbrock).