4Univariate (Single DV) Search Techniques
4.1 Univariate (Single DV)
The term “line search” is often used to mean that the optimization application has a single decision variable. I will use the term univariate, one variable, to indicate a single DV:
The variable x could be a primary, fundamental variable, such as what might be graphed in an f(x) w.r.t. x presentation.
However, the decision variable might be distance along a line that goes through space, and the objective might be to find the point along the line to maximize proximity (minimize distance) to a planet. Using a parametric notation for a line to calculate the (x, y, z) position as a function of parameter “s” from the origin:
Note: At some position (x, y, z) distance along the line from the origin (x0, y0, z0) is S, not s:
However, here the objective is not to minimize distance along the line, but the distance from the line to the point. Then, with the OF to minimize distance to a planet, a point object, at (xp, yp, zp), the optimization statement becomes
Here the DV is not distance along an axis in ...
Get Engineering Optimization now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.