I want to find a value in the range 0-x, using the binary iteration this interval will be halved each iteration but at each iteration I need to solve complex time consuming problem, are there algorithms or approaches faster than the binary iteration algorithm?.
@Ashraf,if you search a nondecreasing,prealocated array of size n,there is no method faster method than binary search which has average and worst complexity O(logn).Maybe you can gain speed by preproccessing the problem you have to solve at each step
Dikeos Mario
FWIW I have always had good success with a modified Newton-Raphson method I keep track of the smallest value I know to be too high and the largest I know to be too small but I only use this information (and interval halving) when the Newton method gives a next value outside of that range. Any method will likely only find local maximums or minimums if it is likely that there are several local max/min you may need to repeat the procedure at different starting points to find the other local max/min.
I don't like most out of the box optimization algorithms but others I know seem to love them. The complexity of the optimization algorithm required depends on the complexity of the problem there really isn't a good 1 size fits all solution for complex optimization problems.
Dear Rick, thank you very much for your useful answer.
Best Regards
Ashraf
There are lots of heuristic optimization algorithms. You may find them on my contributions
Dear Hamid, thank you very much for your answer, I will have a look at your valuable contributions.
Best Regards
Ashraf
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