Consider the following problem min x + f(x) s.t. x in R; where the function f(x) is defined as f(x) = 0 when -1 1

Consider the following problem

min x + f(x)

s.t. x in R;

where the function f(x) is defined as

f(x) = 0 when -1

f(x) =1 when x=1

f(x) =2 when x=-1

f(x) = infinity when x >1 or x<-1

(a) Is the objective function a convex function defined on R? Explain your answer by checking the criterion of convexity.

(b) Find an optimal solution, or explain why there is no optimal solution.