Local Maxima

The science has concerned itself with solving many problems of the world, there is a reason why mathematics is considered as the purest science,
Because it finds a solution so generic that it can be applied to solve problems of all derived sciences, from physics, chemistry, biology to the extremes of sociology,
psychiatry, psychology and even faith. We just have to find a construction of our problem into mathematics.

I did a similar exercise to re-look at a life problem with mathematics, Local Maxima.
In pursuit of finding maxima, using basic human probe analysis, one often comes across a local maxima, and he is not able to proceed further.
The issue is not that he is not probing at all the directions, the issue is just that he is only looking at the immediate turns, which seems to go down hill in any direction it takes.

Dilemma:A dilemma (Greek: δίλημμα “double proposition”) is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. One in this position has been traditionally described as “being on the horns of a dilemma”, neither horn being comfortable. This is sometimes more colorfully described as “Finding oneself impaled upon the horns of a dilemma”, referring to the sharp points of a bull’s horns, equally uncomfortable (and dangerous).

There are multiple ways to find the path towards global maximum, I have tried to list 2 of my applied ones,
1- Genetic Algorithm approach, Introducing a mutation from the current set, and let it compete in the playing field. Having enough variables that mutations can occur, we chose a variable change at random. This helps us identify if there is a chance of getting any better results by changing few things in our current state.

The solution is statistical, We keep mutating, in hope of finding a better solution, and if luck may be so, we will after some rounds.

2- Calculus, Analyze your function, and find its derivative function, see where it gets Grounded to zero. Any place where the derivative function gets grounded is a local minima or maxima. The problem however is how do we know the number of places our derivative gets grounded?
You keep looking at the deriving function, till you reach at the root one, whose derivative is already Zero (Ground). And there is nothing beyond.
Using this, you find the maxima you are looking for, at least the path to it.

The solution is deterministic, but it needs exact formulation of our Maximizing function, which is usually difficult to obtain.

There is no one way to solve a problem, neither is there 1 solution to a problem,
Just a lot of problems for us to try to control in life.

Here is a reference to the image copied from,(Seemed like a good post)

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