MET 503
Applied Optimization – Fall 2015
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 
1/11 
Intro
to optimization Lifeguard
problem 



1/13 
Binary Search 



1/15 
HW #1: Solve Lifeguard
problem using binary search ·
Δx = 30 ·
Exit criteria: o
Change in Δx < 1m and o
Change in T* < 1% ·
Repeat the solution with Δx
= 18 You
can do the problems by hand or with MathCad 
Due: 

Week 2 
1/18 
MLK Holiday 


1/20 



1/22 
Successive Parabolic
Approximations Exit
Criteria Solving
Simultaneous Equations on a TI89 

Due:

Week 3 
1/25 
SnapThrough
Spring problem statement Physical
Problems: o
TwoBar Truss Problem 



1/27 
Local
vs. Global Minima Marching Grid: 2D analogy to binary search Two Variable Monte
Carlo Example 

Due: 

1/29 
Marching
Grid Class Example 


Week 4 
2/1 
Least
Squares Curve Fits 



2/3 
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) Using minimize function in Matlab ·
Find minimum by setting grad f = 0 ·
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 

2/5 
Steepest
Descent Using Binary Search for 1D Minimization 


Week 5 
2/8 

HW #3 Several Methods for
Single Variable Problems Find the minimum values
of test function 2 on page 109 of the notes ·
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: 2/17 

2/10 
Exam
1 Review 



2/12 
Exam 1 


Week 6 
2/15 
Conjugate
Gradient Method 
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: 2/22 

2/17 
Conjugate
Gradient Method 



2/19 
Constraints Exterior
Penalty 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 
Due:
2/26 
Week 7 
2/22 
Constrained Optimization
Problems 
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
Use mathcad minimize function
for 1D search o
Exit criteria (satisfy one) 1.
15 iterations 2.
ΔF < 1% 3.
Δx, Δy
and Δz all less than 1% 


2/24 




2/26 
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 


Week 8 
2/29 
Structural
Optimization 



3/2 
Exterior
Penalty Function 



3/4 
HW #8: Conjugate Gradient
Method Estimate
the minimum value of the bug splatter function (page 231) ·
Use steepest descent starting at x=4, y=1 ·
Use the conjugate gradient method starting at x=4, y=1 Use
the mathcad minimize 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. 

Week 9 
3/7 




3/9 
Interior Penalty Function 
HW #9: Constrained
Optimization Problems ·
Minimize the surface area of a cylindrical can that hold 500
mL of liquid using both interior and exterior penalty function methods o
Use steepest descent with Mathcad minimize function for
1D search. Initial design: D=100mm, H=100mm 
Due: 

3/11 


Week 10 
3/14 



3/16 
Spring Break 


3/18 


Week 11 
3/21 
Design
Variable Linking Semester
Projects Finite
Difference Gradients 



3/23 
Structural
Optimization 
HW #9: 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 Interior Penalty Function (IPF) 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: o
Δx_{1}, Δx_{2} and Δx_{3}
are all less than 1% o
ΔVol < 1% o
25 iterations.
Every 1D search counts as an iteration. 
Due: 

3/25 


Week 12 
3/28 
. 


3/30 




4/1 



Week 13 
4/4 




4/6 
Exam 2 Review 



4/8 
Exam 2 
Exam 2 – Spring 2007 Answer Key 

Week 14 
4/11 




4/13 




4/15 



Week 15 
4/18 
HW #10 Solve
the two variable box problem from HW #8 using finite difference gradients 


4/20 



4/22 

HW #11: Boundary Value Problem from Class using cubic polynomial
as test function. a) Use Mathcad minimize
function to find unknown parameters. b) Verify using steepest descent. You can use either analytical gradients or
finite different gradients. Use
Mathcad minimize function for 1D search 

Week 16 
4/25 
Project Presentations 



4/27 
Project Presentations 



4/29 
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%