MET 503 Applied Optimization – Spring 2018


 Instructor:    Mark French

                      121 Knoy Hall

                      desk:         765-494-7521

                      mobile:      765-714-9382









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






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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




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 co-workers.  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.






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


Intro to optimization

Lifeguard problem







Binary Search


Sample 1-D Functions

Binary Search



Week 2


MLK Holiday



Algorithms for 1-D Search


2-D Lifeguard Problem

Monte-Carlo Method

HW #1:

Solve Lifeguard problem using binary search

·         X0=0

·         Δx = 30

·         Exit criteria:

o    Δx < 1m


o    Change in T* < 1%

·         Repeat the solution with Δx = 18


You can do the problems by hand or with Matlab


Due: 1/22



Successive Parabolic Approximations

Exit Criteria

Solving Simultaneous Equations on a TI-89

Solving Matrix Equations on a TI-89

Tutorial on Solving Simultaneous Equations


Week 3



Snap-Through Spring problem statement

Snap-Through Spring Solution


Physical Problems:

o      Snell’s Law of Refraction

o      Two-Bar Truss Problem

o      Weight on a Spring

o      Maximizing Range of a Projectile

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 homework-like problem.  I want you to identify a potential use of optimization in the world around you.

Due: 1/29



Local vs. Global Minima

Marching Grid: 2-D analogy to binary search


Two Variable Monte Carlo Example


Marching Grid Example


No Class



Marching Grid Class Example

No Class

Week 4


Least Squares Curve Fits





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



The Shopping Mall Problem


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



Steepest Descent Using Binary Search for 1-D Minimization



Week 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 x0=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





Answer Questions



 Exam 1 Review


1-D Review Problems



Week 6


Exam 1


Spring 2007 Exam 1

Spring 2007 Exam 1 Answer Key


Spring 2008 Exam 1

Spring 2008 Exam 1 Answer Key


Due: 2/19



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%







Week 7


Sample 2-D functions


Constrained Optimization Problems


Constrained Lifeguard Problem


Heaviside Step Function

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











Week 8


Structural Optimization


Maximizing Volume of a Box



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 1-D search

o    Exit criteria (satisfy one)

1.     15 iterations

2.     ΔF < 1%

3.     Δx, Δy and Δz all less than 1%






Exterior Penalty Function






Exterior Penalty Function


Week 9







Interior Penalty Function

HW #7:

Rosenbrock Banana Function

·         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






Week 10





Spring Break




Week 11


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 1-D 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.

















Week 12










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 1-D 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%.




Week 13






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( x1 = x2).  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 1-D 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    Δx1, Δx2 and Δx3 are all less than 1%

o    ΔVol < 1%

25 iterations.  Every 1-D search counts as an iteration.







Week 14















Week 15





Solving boundary value problems using optimization – The Ritz method






Week 16


Project Presentations





Project Presentations





Project Presentations

Last Day of Class










No Final




Homework        15%

Exam 1             25%

Exam 2             25%

Project              35%



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 human-caused incidents with the ultimate goal of maintaining a safe and secure campus. Let’s review the following procedures:

  • To report an emergency, call 911.
  • To obtain updates regarding an ongoing emergency, and to sign up for Purdue Alert text messages, view


·         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.


  • If we are notified of a Shelter in Place requirement for a tornado warning, we will suspend class and shelter in the lowest level of this building away from windows and doors.


  • If we are notified of a Shelter in Place requirement for a hazardous materials release, or a civil disturbance, including a shooting or other use of weapons, we will suspend class and shelter in our classroom, shutting any open doors or windows, locking or securing the door, and turning off the lights.


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., x-y or n-t) and location for the various problem types.



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 multi-communication layers at http://www.pu




Review the Emergency Procedures Guidelines

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.



"Shots Fired on Campus: When Lightning Strikes," is a 20-minute active shooter awareness video that

illustrates what to look for and how to prepare and react to this type of incident. See:

(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




Reference the Emergency Preparedness web site for additional information: