Consider the problem min ex1+x2 x2 ≥ e−x1 x1 ≥ 1 Find all local minima by considering the four cases defined by setting subsets of {μ1, μ2} to zero. Be sure to check that the regularity condition is...

Consider the problem

min ex1+x2

x2 ≥ e−x1

x1 ≥ 1

Find all local minima by considering the four cases defined by setting subsets of {μ1, μ2} to zero. Be sure to check that the regularity condition is

satisfied (linear indepedence of the constraint function gradients). Do any

of the minima satisfy the sufficient conditions for a global optimum? Hint:

g1(x1, x2) = e−x1 − x2 is convex.