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Descent-ascent algorithm to find stationary points f(x,y)

Author:Roman Chijner
  • Coordinate descent-ascent Algorithm for numerically finding possible local extremas of a function of two variables without using its derivatives by means of sliders in GeoGebra. https://en.wikipedia.org/wiki/Coordinate_descent A comparison of numerical calculations of stationary points for the same function by the methods of solving a system of equations using CAS and the proposed method of coordinate descent or ascent is made. The proposed method of coordinate changes, implemented by sequential changes in the values of the sliders, does not require knowledge of the explicit form of the function and its derivatives. This comparison is necessary to evaluate the accuracy of the proposed method. -The method of X, Y -coordinate changes (descent-ascent Algorithm ) is adapted for GeoGebra. -In the case of saddle points, the method was developed by me - I did not find corresponding numerical methods in the literature. The considered method of iterative coordinate ascent-descent for the considered functions has the property of convergence for finding local extrema! The book contains examples of using the algorithm to find local extrema for explicitly defined functions. In these cases, singular points can be found independently using a numerical solution of systems of partial differential equations (in CAS GeoGebra). Comparison of the results for these examples shows good convergence and high accuracy of the proposed algorithm. Thus, the proposed algorithm can be used to solve optimization problems for which there is no explicit definition of the function, i.e. the analytical formula of the function is unknown, it can be specified numerically at each point (x,y). -The algorithm is used to find stationary points of the interference field distribution behind a slit illuminated by an incident plane wave.
    • Descent-ascent algorithm to find stationary points f(x,y)

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