Introduction to Optimum Design, 2nd Edition

4 Optimum Design Concepts

Upon completion of this chapter, you will be able to:

• Define local and global minima (maxima) for unconstrained and constrained problems

• Write optimality conditions for unconstrained and constrained problems

• Check optimality of a given point for unconstrained and constrained problems

• Solve first-order optimality conditions for candidate minimum points

• Check convexity of a function and the design optimization problem

• Use Lagrange multipliers to study changes to the optimum value of the cost function due to constraint variations

EXAMPLE 4.2 Graphical Representation of Constrained Minimum

Solve the optimum design problem formulated in terms of variables x and y as: minimize f(x,y) = (x − 10)² + (y − 8) ...