ISyE 6663 Optimization III
Spring 2003
Assignment 7
Issued: April 15, 2003
Due: April 24, 2003
Problem 1
Nocedal and Wright, Problem 12.3
Problem 2
Nocedal and Wright, Problem 12.4
Problem 3
Nocedal and Wright, Problem 12.5
Problem 4
Nocedal and Wright, Problem 12.13
Problem 5
Nocedal and Wright, Problem 12.14
Problem 6
Nocedal and Wright, Problem 12.17
Problem 7
Nocedal and Wright, Problem 12.18
Problem 8
It matters how the constraints are formulated: Consider the problem
min f(x)
s.t. h(x)=0
where h(x)=(h1(x),...,h
m(x)). Suppose that x∗is a local minimum and that ∇f(x∗)= 0. Show
that x∗is also a local minimum of the problem
min f(x)
s.t. h(x)2
2=0
but that there is no Lagrange multiplier for this problem corresponding to x∗.