MET 503
Applied Optimization – Spring 2017
Instructor:
Mark French
121
Knoy Hall
desk: 7654947521
mobile: 7657149382
email: rmfrench@purdue.edu
Syllabus:

Date 
Topic 
Homework
(10 pts/problem) 
Due Assignments are due by 5:00 on the day listed, either in class or
at my office (121 Knoy) 
Week 1 
1/9 
Intro
to optimization Lifeguard
problem 



1/11 



1/13 
Binary
Search 
HW #1: Solve Lifeguard
problem using binary search ·
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: 1/20 
Week 2 
1/16 
MLK Holiday 


1/18 



1/20 
Successive Parabolic
Approximations Exit
Criteria Solving
Simultaneous Equations on a TI89 


Week 3 
1/23 
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: 1/30 

1/25 
Local
vs. Global Minima Marching Grid: 2D analogy to binary search Two Variable Monte
Carlo Example 



1/27 
Marching
Grid Class Example 


Week 4 
1/30 
Least
Squares Curve Fits 



2/1 
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: 2/10 

2/3 
Steepest
Descent Using Binary Search for 1D Minimization 


Week 5 
2/6 

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: 2/22 Note – This dues date
was moved back from 2/17 

2/8 
Exam
1 Review 



2/10 
Exam 1 

Due 2/18 
Week 6 
2/13 
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% 
Due: 2/27 


2/15 



2/17 


Week 7 
2/20 
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:
3/5 

2/22 




2/24 



Week 8 
2/27 
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:
3/20 

3/1 
Exterior
Penalty Function 



3/3 
Constraints Exterior
Penalty Function 


Week 9 
3//6 
No Class 



3/8 
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: 3/24 

3/10 


Week 10 
3/13 



3/15 
Spring Break 


3/17 


Week 11 
3/20 
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: 3/29 

3/22 




3/24 


Week 12 
3/27 


3/29 




3/31 

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: 4/8 
Week 13 
4/3 




4/5 
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: 4/18 


4/7 


Week 14 
4/10 




4/12 




4/14 



Week 15 
4/17 



4/19 
Solving
boundary value problems using optimization – The Ritz method 



4/21 

No
Class 

Week 16 

Project Presentations 




Project Presentations 




Project Presentations 
Last Day of Class 









No Final 

Links:
Wikipedia Article on Optimization
Wikipedia Article Least Squares Curve Fits
Wikipedia Article on Steepest Descent (Gradient
Descent)
Grading
Homework 15%
Exam
1 25%
Exam
2 25%
Project 35%