Nonlinear Regression Modeling for Engineering Applications by Rhinehart R. Russell;

Author:Rhinehart, R. Russell;
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2015-09-28T00:00:00+00:00

10.3 Gradient-Based Optimization

Gradient-based optimizers are powerful and common, but have undesirable attributes as well.

Gradient-based optimizers evaluate the local slope of the surface to determine what direction is downhill. The steepest downhill direction may not be aligned with a DV axis. Accordingly, there will be a slope for each axis. The slope, of course, is the partial derivative of the OF value with respect to each DV:

10.1

In Equation 10.1 the subscript i represents the DV number. For an M dimension application (one with M DVs) there are M partial derivatives to define the slope.

If one could generate an equation to represent the derivative, the estimate of the slope, solving the equation is a computer procedure. If there are M number of DVs then there are M + 1 number of functions to be evaluated, one for the OF and M for the slopes. However, the function might not provide a convenient or tractable form for solving the derivative analytically. Numerical estimates are usually used.

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