MET 5810 Applied Optimization

MET 5810 Applied Optimization

Instructor: Mark French

138 Knoy Hall

desk: 765-494-7521

mobile: 765-714-9382

e-mail: 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
1/8	Intro to optimization Sample 1-D Functions Monte-Carlo Method Lifeguard problem	HW #1: 1 - Solve lifeguard problem using Monte-Carlo method and Mathcad 2 – Find Minimum of Example Function 1 using Monte Carlo 3 – Find Minimum of Example Function 2 Using Monte Carlo Since this homework set has already been handed in, here’s the answer key.	1/15
1/10	Binary Search	HW #2: 1 - Solve lifeguard problem using binary search Stop when the change in either the objective function or the estimate of x* is less than 1%. 2 – Solve lifeguard problem using successive parabolic approximations. X0=0, dx=10. Stop when the change in approximate solutions is less than 0.25 feet or 8 iterations, whichever comes first.	1/17 Lifeguard problem using parabolic approximations
1/15	Successive Parabolic Approximations Exit Criteria Solving Simultaneous Equations on a TI-89 Solving Matrix Equations on a TI-89 Tutorial on Solving Simultaneous Equations	HW #3: 1 – Solve snap-through spring problem graphically using Mathcad. Report both local and global minima. 2 – Solve snap-through spring problem using successive parabolic approximation, x0=0, dx=0.5. Stop when the change in x between iterations is less than 1% or 5 iterations, whichever comes first. 3 – Solve snap through problem when x0=3 and dx=0.5. Use exit criteria from problem 2 4 – What happens when x0=1 and dx=0.5?	1/22 Snap through spring problem
1/17	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	HW #4: 1 – Find the path through an equilateral glass prism using Snell’s law of refraction 2 – Find the path through the prism by minimizing the optical path length (η=3/2). Use the method of your choice Description of Prism Problem	1/24 Prism problem
1/22	Local vs. Global Minima Marching Grid: 2-D analogy to binary search Two Variable Monte Carlo Example Marching Grid Example	HW #5: 1 – Solve the bungee problem using the Monte Carlo method. Use 25 random number pairs. 2 – Solve the bungee problem using the marching grid method. Use dx=dy=1 to start. Stop when the change in x and y is less than 10%.	1/31 (turn hw in at the end of the class period) Bungee problem – analytical solution
1/24	Bungee Jump Problem using 2-D Marching Grid
1/29	Exam 1 Review 1-D Review Problems Note: this PDF contains solutions using derivatives. We haven’t gone over this yet in class and derivatives won’t be on the exam.		Two variable gradient example
1/31	Exam 1 Spring 2007 Exam 1 Spring 2007 Exam 1 Answer Key Spring 2008 Exam 1 Spring 2008 Exam 1 Answer Key	In-Class, Open Notes, Bring Your Calculator	Two variable unconstrained study problem
2/5	No Class
2/7	No Class
2/12	Sample 2-D functions Constrained Optimization Problems Constrained Lifeguard Problem	HW #6: Structural optimization problem with a single constraint 1 – Use Monte Carlo method with 50 different combinations of x₁ and x₂ 2 – Use marching grid. Pick starting points x₁ = 0 and x₂ = 0.5 inch. Select your own grid size. Stop when reducing the step size decreases the volume of the structure by less than 5%. For both problems, create a pseudo-objective function to transform the constrained problem into an unconstrained problem. Remember that wall thickness has to be positive.	2/19 Constrained 2-D problem using solve block
2/14	Maximizing Volume of a Box Exterior Penalty Function Heaviside Step Function
2/19
2/21	Addition of a buckling constraint	HW #7 Repeat the problem in HW #6 with the addition of an Euler buckling constraint (K=1). Assume an outer tube diameter of 2 inches rather than 3 inches.	2/28
2/26	Addition of third design variable Derivatives and Gradients Gradient Example	HW #8 Repeat the two bar truss problem from HW #7, but allow the two wall thickness to very independently. The three design variables are: joint location, thickness of tube 1 and thickness of tube 2	3/7
2/28	Steepest descent method for unconstrained minimization
3/4	No Class
3/6	No Class
3/11	Spring Break
3/13	Spring Break
3/18
3/20
3/25
3/27
4/8
4/10
4/15
4/17
4/22
4/24

Links:

Wikipedia Article on Optimization

e-optimization community

Wikipedia Article Least Squares Curve Fits

Wikipedia Article on Steepest Descent (Gradient Descent)

Grading

Homework 15%

Exam 1 25%

Exam 2 25%

Project 35%

Extra Credit: As with my other classes. Bring in some example from the real world and successfully connect it with the topics from the class. Each demonstration will add two points to your final course average. Each student may do two demonstrations during the semester.