Engineering Analysis/Minimization

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Engineering Analysis

Before reading this chapter, the student should know what minimization is, and how to minimize a function. Students should also know partial differentiation, and how to solve systems of equations.

[edit] Khun-Tucker Theorem

The Khun-Tucker Theorem is a method for minimizing a function f(x) under the constraint g(x). We can define the theorem as follows:

Where Λ is the lagrangian vector, and < , > denotes the scalar product operation. We will discuss scalar products more later. If we differentiate this equation with respect to x first, and then with respect to Λ, we get the following two equations:

We have the final result:

x = A^T[AA^T] ^{− 1}b