Method 5:Hill Climbing Technique

                  Hill climbing is a technique for certain classes of optimization problems.This Methode is used by newton to find roots. The idea is to start with a sub-optimal solution to a problem (i.e., start at the base of a hill) and then repeatedly improve the solution (walk up the hill) until some condition is maximized (the top of the hill is reached).
Hill-Climbing Methodology
1. Construct a sub-optimal solution that meets the constraints of the problem
2. Take the solution and make an improvement upon it
3. Repeatedly improve the solution until no more improvements are necessary/possible

                One of the most popular hill-climbing problems is the network flow problem. Although network flow may sound somewhat specific it is important because it has high expressive power: for example, many algorithmic problems encountered in practice can actually be considered special cases of network flow. After covering a simple example of the hill-climbing approach for a numerical problem we cover network flow and then present examples of applications of network flow.