MET 503
Applied Optimization – Spring 2018 
Instructor:
Mark French 
121
Knoy Hall 
desk: 7654947521 
mobile:
7657149382 
email: rmfrench@purdue.edu 

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 

8:00 AM 





8:30 AM 





9:00 AM 





9:30 AM 


Office Hours 


10:00
AM 





10:30
AM 
MET 503 

MET 503 

MET 503 
11:00
AM 
Knoy B031 

Knoy B031 

Knoy B031 
11:30
AM 





12:00
PM 





12:30
PM 
MET 213 

MET 213 

MET 213 
1:00 PM 
WTHR 320 

WTHR 320 

WTHR 320 
1:30 PM 





2:00 PM 





2:30 PM 





3:00 PM 





3:30 PM 





4:00 PM 





4:30 PM 





5:00 PM 






Official
office hours are in green.
However, my door is open pretty much whenever I'm in the office. If the door is open, you're welcome to stop
by. If, for some reason, I'm too busy
to talk with you, we'll make an appointment. When you email me, please include
the following text in the subject line:
MET 503 Applied Optimization 
Honesty 
Homework: I understand that you will often learn more
when working with other people in the class, just I did way back when I was
student. If you work with other people
while solving homework problems, please list those people on your
homework. There is no penalty, but I
do want to get you in the habit of acknowledging coworkers. That is something you should do throughout
your career. 
Exams: It makes sense to do take home
exams in this class since there will be extensive calcuations – more than you
could reasonably do by hand in class.
You may not work with other students on your exams. You also may not look for MATLAB code on
the internet to include on your exam.
I understand that there are extensive libraries of MATLAB code freely
available and that these are very useful resources. It is right that you should use these
resources for routine work. However,
copying code and then handing it in as your own is cheating. Putting your name to someone else’s work
is a clear academic integrity violation and I will not tolarate it. 
Note Pack: There is a note pack for the
class in place of a textbook. The hard
copy is available at Boiler Copy for about $21.00. If you would like an electronic copy as well,
here’s the link.

Date 
Topic 
Homework 
Due Assignments are due by 5:00 on the day listed All
homework, exams and projects should be handed in on Blackboard as single PDF files 
Week 1 
1/8 
Intro
to optimization Lifeguard
problem 



1/10 



1/12 
Binary
Search 


Week 2 
1/15 
MLK Holiday 


1/17 
Algorithms
for 1D Search 
HW #1: Solve Lifeguard
problem using binary search ·
X_{0}=0 ·
Δx = 30 ·
Exit criteria: o
Δx < 1m and o
Change in T* < 1% ·
Repeat the solution with Δx = 18 You
can do the problems by hand or with Matlab 
Due:
1/22 

1/19 
Successive Parabolic
Approximations Exit
Criteria Solving
Simultaneous Equations on a TI89 


Week 3 
1/22 
SnapThrough
Spring problem statement Physical
Problems: o
TwoBar Truss Problem 
Optimization in
Practice: Write
a two page (with pictures) description of some application of optimization –
a process or product in common un. Be
sure to identify the objective function and the design variables. Most practical optimization problems have
constraints, so be sure to describe these as well. Note: Don’t just make up some homeworklike
problem. I want you to identify a
potential use of optimization in the world around you. 
Due: 1/29 

1/24 
Local
vs. Global Minima Marching Grid: 2D analogy to binary search Two Variable Monte
Carlo Example 
No Class 


1/26 
Marching
Grid Class Example 
No Class 

Week 4 
1/29 
Least
Squares Curve Fits 



1/31 
Steepest
Descent Gradient
of Objective Function 
HW #2: 1  Given the two
variable function: ·
Find the minimum value of this function and its location
graphically (3 significant figures) ·
Find minimum by setting grad f = 0 ·
Find minimum using evolution algorithm with Matlab ·
Find the minimum using the fminunc function in Matlab 2 – Solve shopping
mall problem ·
Graphically (4 significant figures) ·
Find minimum by setting grad f = 0 and solving with
whatever Matlab function you want to use ·
Find minimum using evolution algorithm with Matlab ·
Find the minimum using the fminunc function in Matlab 
Find parking place
that minimizes distance walked between four stores. You take a package back to the car after
visiting the third and fourth stores.
All distances are in meters. Due: 2/11 

2/2 
Steepest
Descent Using Binary Search for 1D Minimization 


Week 5 
2/5 

HW #3 Several Methods for
Single Variable Problems Find the minimum
values of test function 2 in Appendix B.
Whenever you need a starting point, use x_{0}=0. ·
Set the derivative equal to zero and solve for x* using
‘fzero’ ·
Find the minimum using Matlab function ‘fminunc’ ·
Find minimum using sequential quadratic approximation ·
Use Monte Carlo / Quadratic hybrid method ·
Use binary search / quadratic hybrid method 
Due: 2/14 

2/7 

Answer Questions 


2/9 
Exam 1 Review 

Due: 
Week 6 
2/12 
Exam 1 

Due: 2/19 

2/14 
HW #4: Solve the Two
Variable Lifeguard Problem using marching grid. ·
Starting point:
x1=50m, x2=50 ·
Initial step size: Δx=30m ·
Exit criteria: o
Δx < 0.5m o
Change in T < 0.5% 


2/16 

Due: 

Week 7 
1/19 
Constrained
Optimization Problems 
HW #5: Least Squares Curve
Fitting 1)
Do a parabolic
curve fit of the following data using Matlab: x y 0 0 1 1 2 1 3 1 Find
the curve fit by setting the gradient equal to zero and solving the resulting
three equations. 2)
Do an exponential curve fit of the following data x y 1 1 2 2 3 3 4 4 Find
the curve fit by setting the gradient equal to zero and solving the resulting
two equations. Note: exponential curve is 
Due: 

1/21 




1/23 



Week 8 
2/26 
Structural
Optimization 
HW #6: Three variable
function ·
Starting Point, x=4, y=8, z=4 ·
Given Δx = Δy = Δz = 1, do 2 steps of
marching grid search ·
Find minimum using steepest descent o
Starting point should be the result of the second step of
marching grid o
Use a MATLAB minimizing function for 1D search o
Exit criteria (satisfy one) 1. 15 iterations 2. ΔF < 1% 3. Δx, Δy and
Δz all less than 1% 
Due: 

2/28 
Exterior
Penalty Function 



3/2 
Constraints Exterior
Penalty Function 


Week 9 
3/5 




3/7 
Interior Penalty Function 
HW #7: ·
Starting point x=2, y=2 ·
Do four iterations of steepest descent ·
Plot F(d) to find d* for each iteration ·
Plot path through design space What is the angle
between successive search directions 
Due: 

3/9 


Week 10 
3/12 



3/14 
Spring Break 


3/16 


Week 11 
3/19 
Conjugate
Gradient Method 
HW #8: Conjugate Gradient
Method Estimate
the minimum value of the bug splatter function (page 205) ·
Use steepest descent starting at x=4, y=1 ·
Use the conjugate gradient method starting at x=4, y=1 Use
the matlab ‘fminunc’ function for the 1D search in both cases. Do
six iterations of each method. Plot
the path through design space of each method.
Please plot both on the same axes for comparison. 
Due: 

3/21 




3/23 


Week 12 
3/26 


3/28 




3/30 

HW #9: Constrained
Optimization Problems ·
Minimize the surface area of a cylindrical can that holds
at least 500 mL of liquid using both interior and exterior penalty function
methods o
Use steepest descent with Matlab ‘fminunc’ function for
1D search. Initial design: D=100mm, H=100mm o
Exit criteria is satisfied when change in f* < 1% or
change in both design variables is < 1%. 
Due: 
Week 13 
4/2 




4/4 
HW #10: Maximize the volume
of a box as shown in class. The
material from which the box is to be cut is 1m wide and 2m long. 1.
Assume the box is square when viewed from the top( x_{1}
= x_{2}). Thus, there are two
design variables. 2.
Allow all three dimensions of the box to vary, so there
will be three design variables. ·
Use the Exterior Penalty Function (EPF) to find the
constrained maximum values for volume. ·
Write out the formal problem statement as we did in
class. ·
Use binary search for the 1D search. Choose an appropriate Δd. ·
Make sure to scale the search direction S using the
magnitude of S as shown in class. ·
Choose an appropriate value for R ·
Exit criteria – when any of these three requirements is
satisfied: o
Δx_{1}, Δx_{2} and Δx_{3}
are all less than 1% o
ΔVol < 1% 25 iterations. Every 1D search counts as an iteration. 
Due: 


4/6 


Week 14 
4/9 




4/11 




4/13 



Week 15 
4/16 



4/18 
Solving
boundary value problems using optimization – The Ritz method 



4/20 



Week 16 

Project Presentations 




Project Presentations 




Project Presentations 
Last Day of Class 









No Final 

Grading 
Homework 15% 
Exam
1 25% 
Exam
2 25% 
Project 35% 
Safety: 
As we begin this semester I want to take a few minutes and
discuss emergency preparedness. Purdue University is a very safe campus and
there is a low probability that a serious incident will occur here at Purdue.
However, just as we receive a safety briefing each time we get on an
aircraft, we want to emphasize our emergency procedures for evacuation and
shelter in place incidents. Our preparedness will be critical if an
unexpected event occurs. 

Emergency
preparedness is your personal responsibility. Purdue University is continuously
preparing for natural disasters or humancaused incidents with the ultimate
goal of maintaining a safe and secure campus. Let’s review the following
procedures: 



·
There are nearly 300 Emergency Telephones
outdoors across campus and in parking garages that connect directly to the
Purdue Police Department (PUPD). If you feel threatened or need help, push
the button and you will be connected immediately. 

·
If we hear a fire alarm, we will
immediately suspend class, evacuate the building, and proceed
outdoors, and away from the building. Do not use the elevator. 




Course Objectives: 

Upon successful
completion of this course, the student should be able to: 

1. Distinguish between problems
requiring a Statics solution and problems requiring a Dynamics solution (i.e.,
Bodies that require a Statics solution have no acceleration.) 

2. Identify the different types of
dynamics problem (i.e., Kinematics, Kinetics, Rigid Body, Particle). 

3. Select the appropriate solution
method for the different problem types (i.e., Kinematics, Equation of Motion,
Work/Energy Principles, Conservation of Energy, Impulse/Momentum, and
Conservation of Momentum). 

4. Properly apply each of the solution
methods. 

5. Properly construct motion diagrams
for the solution of Kinematics problems. 

6. Properly draw supporting diagrams for
Kinetics problems (i.e., Free Body Diagram, Kinetic Diagram, Impulse/Momentum
Diagram, etc.). 

7. Properly calculate the mass moment of
inertia for basic and composite shapes. 

8. Select the appropriate coordinate
system type (i.e., xy or nt) and location for the various problem types. 
EMERGENCY PREPAREDNESS SYLLABUS ATTACHMENT 

EMERGENCY NOTIFICATION PROCEDURES are based on a
simple concept – if you hear a fire alarm 
inside, proceed outside. If you hear a siren outside,
proceed inside. 
·
Indoor Fire
Alarms mean to stop class or research
and immediately evacuate the building. 
o
Proceed
to your Emergency Assembly Area away from building doors. Remain outside until police, fire, or other emergency response personnel
provide additional guidance or tell you it is safe to leave. ·
All Hazards
Outdoor Emergency Warning Sirens mean to immediately seek shelter (Shelter in Place) in a safe location within the closest building. 
This course of action may need to be taken during a
tornado, a civil disturbance including a 
shooting or release of hazardous materials in the
outside air. Once safely inside, find out more 
details about the emergency*. Remain in place until police, fire, or other emergency response 
personnel provide additional guidance or tell you it
is safe to leave. 
*In both cases, you should seek additional
clarifying information by all means possible…Purdue Emergency 
Status page, text message, email alert, TV, radio,
etc…review the Purdue Emergency Warning Notification 
System multicommunication layers at http://www.pu
rdue.edu/ehps/emergency_preparedness/warningsystem. 
Html 

EMERGENCY RESPONSE PROCEDURES: 
• Review the Emergency
Procedures Guidelines 
https://www.purdue.edu/emergency_preparedness/flipchart/index.html 
• Review the Building
Emergency Plan (available on the Emergency
Preparedness website or from the 
building deputy) for: 
o evacuation routes, exit points,
and emergency assembly area 
o when and how to evacuate the
building. 
o shelter in place procedures and
locations 
o additional building specific procedures and requirements. 

EMERGENCY PREPAREDNESS AWARENESS VIDEOS 
• "Shots Fired on Campus: When Lightning
Strikes," is a 20minute active shooter awareness video that 
illustrates what to look for and how to prepare and
react to this type of incident. See: 
http://www.purdue.edu/securePurdue/news/2010/emergencypreparednessshotsfiredoncampusvideo.cfm 
(Link is also located on the EP website) 
• All Hazards Online Awareness training video (on
Webcert & Blackboard.) A 30 minute computer based 
training video that provides safety and emergency
preparedness information. See the EP website for sign up 
instructions. 

MORE INFORMATION 
Reference the Emergency Preparedness web site for
additional information: 
https://www.purdue.edu/ehps/emergency_preparedness/ 