Homework Assignment #1
MATH 309: Continuous Optimization
Due date: Friday January 24, 2014
1. A company manufactures clay roong tiles and must provide an order of 7800 m2 of these tiles for
several new houses. Two different types of tiles can be used: mod
Homework Assignment #2
MATH 309: Continuous Optimization
Due date: Friday February 7, 2014
1. The method of steepest descent applied to the problem
min f (x) = 4x2 + x2
1
2
xR2
generates a sequence of points cfw_xk .
(1)k
.
4
(b) What is the minimizer x o
Homework Assignment #4
MATH 309: Continuous Optimization
Due date: Friday March 7, 2014
1. Apply Newtons method to maximize the function
f (x) = 4x1 x2 5x2 2x4 x2 .
1
2
Compute the rst two iterates by hand, starting from the initial point x0 = [0, 0]T . R
Homework Assignment #5
MATH 309: Continuous Optimization
Due date: Friday March 21, 2014
1. Text page 353, Exercise 12.16.
2. (Facility location problem) A company plans to build a number of new service centers that serve 6
clients at the following known
Homework Assignment #3
MATH 309: Continuous Optimization
Due date: Friday February 21, 2014
1.
(a) By hand, apply two iterations of the method of steepest descent with an exact line search to
minimize the function
f (x) = (x1 1)2 + x3 x1 x2 ,
2
using the
Homework Assignment #6
MATH 309: Continuous Optimization
Due date: Friday April 4, 2014
1. (This question originally appeared on Homework #5, but has been moved here in slightly modied form)
Consider the problem
min f (x) = x2 + x2 x2 + 2x1 x2 + x4 + 8x2