Optimization Toolbox
For Use with MATLAB
Computation Visualization Programming
Users Guide
Version 2
How to Contact The MathWorks:
508-647-7000 508-647-7001 The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098
http:/www.mathworks.com ftp.mathworks
Tsinghua University
Mathematical Programming
Reference Solutions to Homework Assignment 3
Problem 1. Reformulate the following two problems as the standard from of LP.
(1)
min
s.t.
|x| + |y|
x + y 2,
x 3.
Solution: Let
x1 =
|x| + x
,
2
x2 =
|x| x
,
2
x3 =
Tsinghua University
Zhang Liping
Math. Prog., Spring 2016
Feb 22 & 25, 2016
Homework Assignment 1: Due Thursday, March 10
Problem 1. Chins Ice Cream Co. is producing three flavors of ice cream: vanilla, mint chip,
and chocolate. These products are manufac
Tsinghua University
Mathematical Programming
Reference Solutions to Homework Assignment 2
Problem 1. Let f C 2 . Then f is convex over a open convex set if and only if the
Hessian matrix of f is positive semi-definite throughout .
Problem 2. Please refer
Tsinghua University
Math. Prog., Spring 2016
Zhang Liping
March 10 & 14, 2016
Homework Assignment 3: Due Thursday, March 24
Problem 1. Reformulate the following two problems as the standard from of LP.
(1)
min
|x| + |y|
s.t.
x + y 2,
x 3.
(2)
max
3x 2y +
Tsinghua University
Math. Prog., Spring 2016
Zhang Liping
March 24 & March 31
Homework Assignment 5: Due Thursday, April 7
Problem 1. a) Using the Two-Phase Simplex method, solve:
minimize
subject to
2x1 + 3x2 + 2x3 + 2x4
x1 + 2x2 + x3 + 3x4 = 3
x1 + x2 +
Tsinghua University
Math. Prog., Spring 2016
Zhang Liping
March 21 & March 24
Homework Assignment 4: Due Thursday, March 31
Problem 1. Consider a system of m linear equations in n nonnegative variables, say
Ax = b, x 0.
Assume the right-hand side vector b
Tsinghua University
Zhang Liping
Math. Prog., Spring 2016
Feb 29 & March 3-7
Homework Assignment 2: Due Thursday, March 17
Problem 1. Let f C 2 . Then f is convex over a open convex set if and only if the
Hessian matrix of f is positive semi-definite thro
Tsinghua University
Mathematical Programming
Reference Solutions to Homework Assignment 1
Problem 1. Chins Ice Cream Co. is producing three flavors of ice cream: vanilla, mint chip,
and chocolate. These products are manufactured using common ingredients: