Optimization
Designing systems that optimize a set of metrics subject to constraints.
The optimization process
minimize f(x) subject to x ∈ X
Minimize f(x) can be replaced by maximize f(x)
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 Design no
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Design +> Initial+>Evaluate +>Good?
Specifications  Design  Performance  
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Final
Design
Optimize with respect to data, as intuition can be misleading.
Translating real world problems
There are some books describing the process to transform real world optimization problems to optimization problems
 Optimization: Algorithms and Applications (R.K. Arora)
 Optimization Concepts and Applications in Engineering (2nd edition, A. Keane, P. Nair)
 Computational Approaches for Aerospace Design (P.Y. Papalambros, D.J. Wilde)
 Principals of Optimal Design (Cambridge University Press, 2017)
Constraints
Constraints can be numerical (for example x ⋝ 4) but should always include the boundary (in the example 4). Excluding it (x > 4), the solution can move infinitely close to 4 without ever reaching it, which means no solution can be found.
Critical Points
A function f(x) may have a global minimum but may have multiple local minima. A zero derivative is a necessary condition for a local minimum but not a sufficient condition. The second derivative has to be >0, so the point is at the bottom of the bowl.