find an optimal value for t(time) on interval [t_min, t_max]

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I want to find minimum time (t) between the interval [t_min, t_max]. I have found different algorithms, like steepest descent method, simplex method. And I am not sure how to approach this methods, say steepest descent algorthim, and how to select the tolerance value. so any help would be appreciated if I get how to implement steepest descent method to find optimal t on the interval [t_min,t_max].
Thanks in advance
Hashir
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Hashir Roshin Valiya Parambil
@sam chak, Suppose, an object needs to start from one point and reach at the target, with minimal energy consumption. But tmin is lower limit for which the travel is not feasible but tmax is more expensive. I need between them.

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Accepted Answer

Sam Chak
Sam Chak on 8 Jul 2022
I think I get what you mean. However, without understanding the nature of your problem, it is difficult to give a particular suggestion. Try reading about Brachistochrone curve and the Calculus of variations.
  2 Comments
Sam Chak
Sam Chak on 8 Jul 2022
Edited: Sam Chak on 8 Jul 2022
Okay @Hashir Roshin Valiya Parambil. I understand your problem.
Since you understand the mathematics of Calculus of Variations and the Brachistochrone problem, I presume that you are really good at math but that doesn't solve your problem.
If this is 2D flat surface problem, I guess you need to find the shortest path to the target location, and naturally, that will be the minimum fuel consumption required. Read about the following:
  1. Travelling salesman problem
  2. Dijkstra's algorithm
  3. A* search algorithm

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