HW 5

Optimization methods 2011

1. 13.5, 13.9 (graph the solution), 15.3.

2. Find

min_{x∈R_{2}} f(x), f = x_{1}^{2} + x_{2}^{2}, subject to x_{1} − x_{2} = 1

using:

(a) quadratic penalty, take μ = 1, 10, 50,

(b) absolute value (non-smooth) penalty, take μ = 1/2, 1, 10 (you may use other values)

(c) augmented Lagrangian, start with the point λ_{0} = 0, μ_{0} = 1.