GaussOptimization.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Algorithms.Other
{
    /// <summary>
    /// The Gaussian method (coordinate descent method) refers to zero-order methods in which only the value
    /// of the function Q(X) at different points in the space of variables is used to organize the search
    /// for the extremum. This reduces the overall computational cost of finding the extremum. Also in
    /// the Gaussian method, the procedures for finding and moving the operating point are simplified as
    /// much as possible.
    /// </summary>
    public class GaussOptimization
    {
        /// <summary>
        /// Implementation of function extremum search by the Gauss optimization algorithm.
        /// </summary>
        /// <param name="func">Function for which extremum has to be found.</param>
        /// <param name="n">This parameter identifies how much step size will be decreased each iteration.</param>
        /// <param name="step">The initial shift step.</param>
        /// <param name="eps">This value is used to control the accuracy of the optimization. In case if the error is less than eps,
        /// optimization will be stopped.</param>
        /// <param name="x1">The first function parameter.</param>
        /// <param name="x2">The second function parameter.</param>
        /// <returns>A tuple of coordinates of function extremum.</returns>
        public (double, double) Optimize(
            Func<double, double, double> func,
            double n,
            double step,
            double eps,
            double x1,
            double x2)
        {
            // The initial value of the error
            double error = 1;

            while (Math.Abs(error) > eps)
            {
                // Calculation of the function with coordinates that are calculated with shift
                double bottom = func(x1, x2 - step);
                double top = func(x1, x2 + step);
                double left = func(x1 - step, x2);
                double right = func(x1 + step, x2);

                // Determination of the best option.
                var possibleFunctionValues = new List<double> { bottom, top, left, right };
                double maxValue = possibleFunctionValues.Max();
                double maxValueIndex = possibleFunctionValues.IndexOf(maxValue);

                // Error evaluation
                error = maxValue - func(x1, x2);

                // Coordinates update for the best option
                switch (maxValueIndex)
                {
                    case 0:
                        x2 -= step;
                        break;
                    case 1:
                        x2 += step;
                        break;
                    case 2:
                        x1 -= step;
                        break;
                    default:
                        x1 += step;
                        break;
                }

                // Step reduction
                step /= n;
            }

            return (x1, x2);
        }
    }
}