Section 18.104.22.168: Algorithm for Unbounded Search
||lower bound specified for optimisation
||upper bound specified for optimisation
||starting point for search (should be feasible:
xL < x0 < xU)
||starting step size
||acceleration factor (greater than 1)
and a procedure to evaluate f(x)
- Construct 3 initial search points at
If either of the adjacent points crosses xL or xU reset the value to the constraint.
- Calculate the objective function at each of the 3 points and identify which
has the smallest value.
- If the middle point is the minimum we have a bounded search range between the leftmost and rightmost points; exit.
- Otherwise, iteratively search in the direction of descent:
+ if the rightmost point was the minimum, Set the current step size = initial step size
- if the leftmost point was minimum.
- If the point furthest in the direction of search is on a constraint boundary
(xL or xU),
we have a bounded search range between that point and the one next to it; exit.
- redefine current step size =
current step size; this provides acceleration of the search
- create a new search point beyond the rightmost (+) or leftmost(-) by the new current step size (but do not pass the constraint boundary);
calculate the objective at this point and with the adjacent two points define a new search range.
- Find the point in the new search range with the minimum objective value.
- If it is the middle one, we have a bounded search range,
- otherwise repeat from 4(a) until a bounded search range is found, or too many iterations.
Return to Section 5.3.2
Return to Section 5.3 Index
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Last modified: Tue Aug 25 11:01:25 BST