CATALOG DATA:
Introduction to basic optimization techniques for mechanic design problems.

TEXTBOOK:
Venkataraman, P., Applied Optimization with MATLAB Programming, John Wiley and Sons, New York, 2002

GOALS:
This course is designed to introduce the optimization techniques and practices by engineers in the design of mechanical systems. Students are tasked with implementing optimization strategies in software on the computer. These implementations are then tested on actual engineering design problems to evaluate their utility. In addition to writing their own optimization software students have an opportunity to apply state of the art optimization software to engineering design problems. Students address both design analysis and design synthesis in course assignments.

Topics:

• Introduction and Sample Engineering Problems
• Unconstrained Nonlinear Optimization - Single Variable Functions
  Properties and Optimality, Region elimination methods
  Polynomial estimations, Newton and Secant Methods
• Unconstrained Nonlinear Optimization - Functions of Several Variables
  Properties, Optimality Criteria
  Direct Search Methods
         Simplex, Pattern Search, Conjugate Directions
  Gradient Based Methods
         Cauchy and Newton Methods,
         Conjugate Gradient and Quasi-Newton Methods
  Numerical Approximation and Scaling
• Constrained Linear Optimization - Simplex Method, Sensitivity
• Constrained Nonlinear Optimization
  Optimality Criteria, Lagrange Multipliers
  Kuhn-Tucker Conditions
  Feasible Directions Method
  Generalized Reduced Gradient Method

Computer Usage:
In addition to writing their own optimization software students in AME-544 have an opportunity to apply state of the art optimization software to engineering design problems. The Matlab Optimization Toolbox used in the course includes a SQP (Sequential Quadratic Programming) optimization algorithm. Design studies that students have addressed are listed below:

Optimization of a Gas Pipeline Transmission System.
Design of Structural Control Systems.
Spring/Mass System Design Optimization.
Minimum Weight Structural Design.

ABET category content as estimated by faculty member who prepared the course description:
Engineering Science: 0 credits
Engineering Design: 3.0 credits or 100%

Prepared by: Professor John E. Renaud
Last Update: June 8, 2004

 

Direct comments, questions, and corrections to amedept@nd.edu