Description
The method is based on dividing the current segment [a, b], which contains the desired extremum, into two equal parts with the subsequent selection of one of the halves, in which the minimum (maximum) is localized as the next current segment. The extremum is localized by comparing two values of the optimality criterion at points spaced ε/2 from the midpoint of the segment, where ε is the error of solving the optimization problem.
If R(x+ε/2)>R(x-ε/2), then the maximum is located on the right half of the current segment [a, b], otherwise - on the left. The search process ends when the segment [a, b] reaches the specified error e ε.
The method’s drawbacks include its performance for only one-extremal functions R (x) (i.e., those that contain one extremum of the type we we are looking for in the task), since in other cases when comparing two criteria at adjacent points it is impossible to correctly select the next interval where the minimum (maximum) is located.
The program contains the value X of the equation F (X) = 0.0001-X-0.25*3.7*(exp(0.5*X)-1), but this equation can be changed to another equation.
ATTENTION
We can write this program in the programming language you need and with the program conditions that you set, for this you need to order the program (the Order button) and we will contact you shortly.
The program code is in the archive with the program as a separate project.