ME 517
OPTIMIZATION IN DESIGN

Course Description

Optimization methods as applied to engineering design, theory and application of nonlinear optimization techniques for multivariate unconstrained and constrained problems. Model boundedness and sensitivity.

Topics

• Modeling, objective functions, maxima and minima, necessary and sufficient conditions for an unconstrained minimum
• Constrained optimization, constraint activity and monotonicity analysis
• Unconstrained univariate and multivariate optimization
• Constrained multivariate optimization: General concepts, Lagrange multipliers, KKT conditions, linear programming, generalized reduced gradient method
• Iterative Numerical Methods: Feasible directions, interior and exterior penalty functions, augmented Lagrange multiplier method
• Robust design

Learning Outcomes

The student, upon completion of this course, will be able to:

• Construct optimization models for engineering design problems in terms of design variables, feasible region, objective function, and equality/inequality constraints.
• Use monotonicity analysis, graphical representation, and elimination techniques jointly to examine the adequacy and find the analytical solutions of the optimization design models.
• Apply optimality conditions (necessary and sufficient) to analytically solve unconstrained/ constrained optimization problems with multiple variants and single objective function.
• Apply Gradient and Newton –based iterative methods to numerically solve unconstrained/constrained optimization problems with multiple variants and single objective function.
• Examine the robustness of the optimization solutions using sensitivity analysis.
• Develop a technical report on an optimization design project based on a real world engineering problem.