Chapter 28 Optimization

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Steepest Descent Method

The steepest descent method use the slope at the initial point and moves down hill.

Equation 28.4.1 New parameter value Calculated from WSS Surface

The computer program can estimate the rate of change of WSS with respect to each parameters (δWSS/δP) by making a small change in each parameter and determining the new WSS. This gives a direction. A linear search in this direction provides the value of h for the lowest WSS. This point becomes the old value and a new search is undertaken. With each iteration the program moves closer to the minimum value of the WSS.

Figure 28.4.1 Contour map of kel versus V showing probable Path of Steepest Descent Method

Advantages of this method

Always 'downhill'
Avoids 'saddle points'
Efficient further from the minimum

Disadvantages of this method

Slower close to minimum
Linear search may cause problems
Might 'zigzag' down valleys

The steepest descent method is not commonly used on its own to perform a nonlinear least squares best-fit but it does form the basis of another more useful method, Marquardt's method. The linear search, zigzaging down valleys and being so slow near the minimum mean that other methods are more efficient.

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