The GoldenSectionLS class performs a line search on 'f(x)' to find a minimal value for 'f'. It requires no derivatives and only one functional evaluation per iteration. A search is conducted from 'x1' (often 0) to 'xmax'. A guess for 'xmax' must be given, but can be made larger during the expansion phase, that occurs before the recursive golden section search is called. It works on scalar functions (see goldenSectionLSTest). If starting with a vector function 'f(x)', simply define a new function 'g(y) = x0 + direction * y' (see goldenSectionLSTest2).
A recursive golden section search requiring only one functional evaluation per call. It works by comparing two center points x2 (given) and x4 computed.
A recursive golden section search requiring only one functional evaluation per call. It works by comparing two center points x2 (given) and x4 computed.
Value parameters
f2
the functional value for the x2 center point
left
whether to search left (true) or right (false) side of last interval
x1
the left-most point
x2
the center point (.618 across for left and .382 across for right)
Perform an exact Line Search (LS) using the Golden Search Algorithm. Two phases are used: an expansion phase (moving the end-point) to find a down-up pattern, followed by a traditional golden section search.
Perform an exact Line Search (LS) using the Golden Search Algorithm. Two phases are used: an expansion phase (moving the end-point) to find a down-up pattern, followed by a traditional golden section search.
Value parameters
x1
the left (smallest) anchor point for the search (usually 0)
xmax
a rough guess for the right end-point of the line search