MET 503
Applied Optimization
Instructor:
Mark French
138
Knoy Hall
desk:
7654947521
mobile: 7657149382
email: rmfrench@purdue.edu
Syllabus:
Date 
Topic 
Homework
(10 pts/problem) 
Due Assignments are due by 4:30 on the day listed at the homework
drop box in Knoy Hall 
1/13 
Intro
to optimization Lifeguard
problem 


1/15 
Binary Search 


1/17 
HW #1: Solve Lifeguard
problem using binary search ·
Δx = 30 ·
Exit criteria: o
Change in x* < 1% o
Change in T* < 1% ·
Repeat the solution with Δx
= 18 You
can do the problems by hand or with MathCad 
Due: 1/24 

1/20 
MLK
Day 

1/22 


1/24 
Successive Parabolic
Approximations Exit
Criteria Solving
Simultaneous Equations on a TI89 
HW #2: 1  Given the 2D
function: ·
Find the minimum value of this function and its location
graphically (4 significant figures) ·
Find the minimum using the minimize function in Mathcad 2 – Solve shopping
mall problem ·
Graphically (4 significant figures) Using
minimize function in Mathcad 
The
Shopping Mall Problem Find parking place
that minimizes distance walked between three stores. You take a package back to the car after
visiting the second store. All
distances are in meters. Due:
1/31 
1/27 
SnapThrough
Spring problem statement Physical
Problems: o
TwoBar Truss Problem 


1/29 
Local
vs. Global Minima Marching Grid: 2D analogy to binary search Two Variable Monte
Carlo Example 
HW #3: Solve the 2D
Lifeguard Problem using marching grid. ·
Starting point:
x0=50m ·
Initial step size: Δx=30m ·
Exit criteria: o
Δx < 0.5m o
Change in T < 0.25%
Due: 2/5 

1/31 
Marching
Grid Class Example 


2/3 
Least
Squares Curve Fits 
HW #4: Least Squares Curve
Fitting 1)
Do a parabolic
curve fit of the following data: 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: 2/10 

2/5 
Steepest
Descent Gradient
of Objective Function 
HW #5: Three variable
function ·
Starting Point, x=4, y=8, z=4 ·
If 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% Due 2/24 

2/7 
Steepest
Descent Using Binary Search for 1D Minimization 


2/10 

HW #6: ·
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 2/24 

2/12 
Exam
1 Review 


2/14 
Exam 1 


2/17 
Conjugate
Gradient Method 


2/19 
Conjugate
Gradient Method 
HW #7: 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. Due: 2/26 

2/21 
Constraints Exterior
Penalty Function 


2/24 
Constrained
Optimization Problems 


2/26 

No Class 

2/28 



3/3 
Structural
Optimization 
HW #8:
Constrained Optimization Problems ·
Minimize the surface area of a cylindrical can that
hold 500 mL of liquid using both interior and
interior penalty function methods o
Use steepest descent with Mathcad minimize function for 1D search. Initial design: D=100mm, H=100mm Due: 3/10 

3/5 
Exterior
Penalty Function 


3/7 
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: 3/14 


3/10 



3/12 
Finite Difference Gradients 
HW #10 Solve the two
variable box problem from HW #8 using finite
difference gradients. Due: 3/14 

3/14 


3/17 


3/19 
Spring Break 

3/21 


3/24 
Design
Variable Linking Semester
Projects 


3/26 
Structural
Optimization 


3/28 
Adding
buckling constraints 
HW #11: Find the minimum weight truss that supports 1000N as
shown. The only design variable is wall
thickness, t. Use any method you wish
for the 1D search. Plot
pseudoobjective function vs. t. E=70 GPa and σ_{max} =
100 MPa. The
outer diameter of the tubes is 75mm. Use finite elements.
The only constraint is maximum stress Due: 4/4. 
Due: 4/18 
3/31 
Literature Review 


4/2 
Literature Review 


4/4 
Literature Review 


4/7 



4/9 



4/11 



4/14 



4/16 
Structural
Optimization 


4/18 
Structural
Optimization Review of
Constraints 
HW #12: Find the minimum weight truss that supports 1000N as
shown. Use any method you wish for the
1D search. Plot pseudoobjective
function vs. t. E=70 GPa and σ_{max} =
100 MPa. The
outer diameter of the tubes is 75mm. Use finite elements. The design variables are wall thickness, t, and
vertical position of the joint between the two elements. Use both stress and buckling constraints. Due: 4/25 
Due: 4/20 
4/21 
Interior Penalty
Function 

4/23 
Interior Penalty
Function 


4/25 

Exam 2 – Spring 2007 Answer Key 
Exam 2 will be a
takehome exam. I will email it to
the class on 4/20. The completed exam
will be due at the beginning of class on 4/23 
4/28 
Project Presentations 


4/30 
Project
Presentations 


5/2 
Project Presentations 










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%