Minimization algorithms steepest-descent method

Steepest descents The steepest descents method is a minimization algorithm in which the line search direction is taken as the gradient of the function to be minimized. The steepest descents method is very robust in situations where configurations are far from the minimum but converge slowly near the minimum (where the gradient approaches zero). 

The iteration process (5.14) together with the linear line search described by formula (5.21) gives us a numerical scheme for the steepest descent method for misfit functional minimization. Thus, this algorithm for the steepest descent method can be summarized as follows ... 

It is very difficult to compare true efficiencies in minimization algorithms. Depending on the sophistication of the program, the machine system used, and other variables difficult to trace, computation times vary widely, even for the same procedure. It would seem that the pattern search method should be considerably faster than the steepest descent method, other things being equal. 

In practical calculations, the steepest descent method produces, with a finite step size, a minimizer in any exactness, where usually some numerically pathological cases should be avoided [12]. A simple algorithm for steps with step size > 0 along the tangent of x(s) can be used... 

Algorithm used for the minimization of mathematical functions (steepest descent, gradient, second-derivative and other methods). In molecular mechanics these are used to minimize the strain energy and thereby optimize the molecular structure (see molecular mechanics). 

A molecular mechanics optimization allo vs partial to full atom flexibility of the protein through an energy minimization of the protein-ligand complexes and can be used for postprocessing of docked poses. In favor of that, various minimization methods ranging from a steepest descent to a genetic algorithm can be used [67]. 

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