The choice of α in Exercise 3 has an analogy in the trust-region L -shaped method in terms of the size of the region Δν . Find a general expression for Δν as a function of α and the solution of (2.1)...

The choice of α in Exercise 3 has an analogy in the trust-region L -shaped method in terms of the size of the region Δν . Find a general expression for Δν as a function of α and the solution of (2.1) with weight α on the regularizing term. Find the corresponding value when α = 1 for Example 1. What updating rule for Δν would be analogous to the rule in Exercise 3d. Starting with Δ1 corresponding to α = 1 , follow that updating rule for the trust-region L -shaped method for Example 1.