IE426 Optimization models and applications
Fall 2008 Homework #1 Solutions
1
Convexity, relaxations, and feasibility (3 pts.)
For each of the following problems, say if it is feasible, and if so, whether its
convex or nonconvex, and why, if necessary and
IE426 Optimization models and applications
Fall 2008 Solution of quiz #2, November 4, 2008
1 Modeling (12 pts.)
A large bank has a set of branches across Pennsylvania. The bank wants to match some
pairs of branches so that each branch in the pair provides
IE426 Optimization models and applications
Fall 2008 Solution of quiz #2, November 4, 2008
1 Modeling (12 pts.)
A large bank has a set of branches across Pennsylvania. The bank wants to match some
pairs of branches so that each branch in the pair provides
IE426 Optimization models and applications
Fall 2008 Quiz #1, September 30, 2008
1 Convexity, relaxations, and feasibility (7 pts.)
Convex functions (2 pts.). Are the following functions convex or not? Fill in the space
with C for convex or N for nonconve
Announcements
IE 426
Optimization models and applications
Cynthia Barnhart (MIT) will give two talks on Optimization in
the Airline Industry.
Lecture 26 December 4, 2008
Today, 3pm, Mohler 453:
Optimization Approaches to Airline Industry Challenges:
Aircr
Application: Least squares approximation
IE 426
Optimization models and applications
Problem: Perform regression analysis on a set of experimental
observations to identify a trend.
A set of (n + 1)-dimensional points
a1 = (a11 , a12 . . . , a1n , b1 ),
a2
Quiz #1
IE 426
Optimization models and applications
September 30 (next Tuesday)
Closed book, no calculators
75 minutes
Subjects:
Lecture 10 September 25, 2008
Linear Programming, Goal Programming
No AMPL
Linear Programming
Convexity, relaxations, lower/up
IE426 Optimization models and applications
Fall 2008 Homework #4 Solutions
1
Nonlinear Programming (5 pts.)
1. Write the Lagrangian function and the KKT conditions for the following
problem (2 pts.):
min y 2x
y x2
x y2
y5
2. Solve the resulting system and
IE426 Optimization models and applications
Fall 2008 Homework #3 Solutions
1
Modeling (6 pts.)
Given a graph G = (V, E ), two nodes s and t of V , and a nonempty proper
subset N of V that contains s but not t, an s t cut is dened as the set C E
of edges w
IE426 Optimization models and applications
Fall 2008 Homework #2 Solutions
1
Modeling (3 pts.)
In an automated library, a robotic bookcase of length l has n shelves (there are
n shelves of length l each, on top of each other). The total height of the book
IE426 Optimization models and applications
Fall 2008 Quiz #1, September 30, 2008
1 Convexity, relaxations, and feasibility (7 pts.)
Convex functions (2 pts.). Are the following functions convex or not? Fill in the space
with C for convex or N for nonconve