The mean squared error minimization smoothing constant's value can be found using a nonlinear optimization process.
Although the linear programming model is effective in many nonlinear optimization circumstances, it is insufficient to accurately model some issues. An illustration would be the isoperimetric problem, which asks you to identify the closed plane curve with the maximum area and a minimization given length. Pappus of Alexandria had access to the solution but not the proof. 340 CE.
The Swiss mathematician Johann Bernoulli challenged himself in 1696 to find the curve that minimizes the time it takes an object to slide, using minimization only the force of gravity, between two nonvertical points. This challenge marked the beginning of the branch of mathematics known as the nonlinear optimization calculus of variations. Along with Johann Bernoulli, the correct answers were also provided by his brother Jakob Bernoulli, the German Gottfried Wilhelm Leibniz, and the Englishman Isaac Newton. (The solution is the brachistochrone.) Many nonlinear algorithms, in particular, heavily rely on Newton's method of solving the problem.
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