Consider the following objective function that is to be minimized: f(x) = ( +8-3) + (21+5-15)....

Transcribed Image Text:

Consider the following objective function that is to be minimized: f(x) = (₁ +8₂-3)² + (21+5₂-15)². 1. Solve the problem analytically. Demonstrate the point you are obtaining is indeed the optimal solution. If the solution is the global minimum demonstrate it is. 2. By "hand", solve the problem using steepest descent method starting from point [0 0]. Use your Brent's polynomial approximation code for the line search with an initial step size for the bracketing of 0.2. Only show the first two iterations of the method. To reduce the number of steps, use a termination tolerance of 0.2. Consider the following objective function that is to be minimized: f(x) = (₁ +8₂-3)² + (21+5₂-15)². 1. Solve the problem analytically. Demonstrate the point you are obtaining is indeed the optimal solution. If the solution is the global minimum demonstrate it is. 2. By "hand", solve the problem using steepest descent method starting from point [0 0]. Use your Brent's polynomial approximation code for the line search with an initial step size for the bracketing of 0.2. Only show the first two iterations of the method. To reduce the number of steps, use a termination tolerance of 0.2.

Answer rating: 100% (QA)

To solve the given objective function analytically we need to find the critical points by taking the partial derivatives with respect to each variable ... View the full answer