Engineering Optimization

Update: September 10th, 2008

This is a basic course in engineering optimization with emphasis on algorithms and applications. By the end of the course, the students are expected to be able to build optimization models of practical problems and solve them using the tools they learnt in class. Ample opportunity will be given to use available optimization computer codes.

The first 5-10 minutes of every lecture will be devoted to answering questions about the previous lectures. Students are urged to utilize this opportunity. Videotaped lectures on VHS format are available for reviewing certain course material. The instructor has also purchased MATLAB Classroom Kit for the students in the class. The students can load the software on their home computer after signing an agreement form and use it for class assignments. The School of Industrial Engineering also has MATLAB on its machines.

Prerequisites

IE 4623 or knowledge of linear programming is a prerequisite to this course. Those who want to brush up their LP background should view tape #5 and/or read Chapter 4 of the text.

Topics

  1. Introduction to Optimization: What is an optimization mode, formulation of optimization models in engineering, classification of optimization problems.
  2. Single Variable Optimization: Optimality criteria, region elimination methods, methods requiring derivatives.
  3. Multi Variable Optimization: Optimality criteria, direct search methods, gradient based methods.
  4. Constrained Optimality Criteria: Lagrange multipliers, Kuhn-Tucker conditions.
  5. Constrained Direct Search: Direct search methods for constrained optimization problems, random search, complex search.
  6. Linearization Methods for Constrained Optimization: Successive LP method, Frank-Wolfe algorithm.
  7. Other Optimization Methods: Penalty Function Method, Method of Feasible Directions, Convex Simplex Method, Reduced Gradient Method.

Required Textbook

G. V. Reklaitis, A. Ravindran and K. M. Ragsdell. Engineering Optimization: Methods and Applications. Wiley, 1983.

Students are expected to be familiar with the basic commands of MATLAB.

Exams, Grading and Homework

There will be two semester exams and a final for this course. Short homework will generally be assigned to illustrate the material in each lecture. Homework is compulsory and late submissions are unwelcome. Reading assignments represent the topics covered in the class during that lecture week. Students are expected to read them at least once before the next week’s lecture.
Course grades will be computed on the following basis:

  • First exam: 20%.
  • Second exam: 25%.
  • Final exam: 30%.
  • Homework: 25%.

Videos

Get the Flash Player to see the wordTube Media Player.

Tape 1: Mathematical Programming, by A. Ravindran.

  • An Introduction (37 minutes).

Tape 2: Unconstrained Optimality Criteria, by A. Ravindran.

  • Single Variable – Optimality Conditions (25 minutes).
  • Convexity & Unimodality (25 minutes).
  • Matrices & Quadratic Forms (25 minutes).
  • Several Variables – Necessary Optimality Conditions (25 minutes).
  • Several Variables – Sufficient Optimality Conditions (25 minutes).

Tape 3: Direct Search Methods, by G. V. Reklaitis.

  • Simplex Search (30 minutes).
  • Pattern Search/Hooke-Jeeves (30 minutes).
  • Conjugate Directions and Powell’s Method (50 minutes).
  • Constrained Direct Search – COMPLEX Method (30 minutes).

Tape 4: Constrained Optimality Criteria, by A. Ravindran.

  • Lagrange Multipliers (30 minutes).
  • Kuhn Tucker Conditions (60 minutes).

Tape 5: Linear Programming, by A. Ravindran.

  • Formulation of LP Models (25 minutes).
  • Graphical Solution of Two Variable LP Problems (25 minutes).
  • Solution of Systems of Equations (25 minutes).
  • Basic Principles of the Simplex Algorithm (25 minutes).
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