This page provides a listing of the topics planned for AAE 550 grouped into 12 modules.
| Module |
Topics |
| 01 |
Class Introduction |
| 02 |
Basic Concepts: Definitions, Optimal Design Problem Statement, Iterative Procedure, Solution Existence and Uniqueness, Kuhn-Tucker Conditions |
| 03 |
Functions of One Variable - Concepts, Newton's Method, and Quadratic Fit, Golden Section Search, Matlab's fminbnd |
| 04 |
Unconstrained Functions in N Variables:
First-Order Methods - Calculating Derivatives, Steepest Descent, Conjugate Direction, Variable Metric (DFP, BFGS);
Second-Order Methods - Newton's Method, Variable Transformation and Scaling; Convergence Criteria, Matlab's fminunc, Excel Solver Add-in |
| 05 |
Linear and Quadratic Programming:
Simplex Method Excel Solver for LP, Matlab's linprog, Quadratic Programming, Matlab's quadprog
|
| 06 |
Constrained Functions in N Variables - Direct Methods: Introductory Concepts, Sequential Linear Programming (SLP), Method of Centers (MoC), Generalized Reduced Gradient (GRG) , Excel Solver Add-in, Sequential Quadratic Programming (SQP), Matlab's fmincon |
| 07 |
Constrained Functions in N Variables - SUMT: Exterior and Interior Penalty Methods, Comparison of Penalty Methods, Constraint Scaling, Augmented Lagrange Multiplier (ALM) Method |
| 08 |
Non-smooth and Global Optimization:
Nelder-Mead Simplex, Simulated Annealing, Genetic Algorithms |
| 09 |
Multiobjective Design: Pareto Optimality and Dominance, Weighted Sum, Weighted Sum, ε-Constraint (Gaming) Approach, Min-Max Approach, Goal Attainment |
| 10 |
Approximation Techniques I: Basic Concepts, Derivative Based, Response Surface Methods, Least squares for Response Surface Coefficients, Design of Experiments, Global Response Surface Approximation, Sequential Response Surface Approximations |
11 |
Multidisciplinary Optimization Introduction:
Decomposition Strategies, Multidisciplinary Feasible and All-at-Once Examples, Collaborative Optimization Example
|
| 12 |
Revisiting the AAE 55000 "Toolbox" and Closing Comments |
|
