Gradient descent

{{task|Optimizations}

{{task|Games}

Typescript

// Using the steepest-descent method to search // for minimum values of a multi-variable function export const steepestDescent = (x: number[], alpha: number, tolerance: number) => {

   let n: number = x.length; // size of input array
   let h: number = 0.0000006; //Tolerance factor
   let g0: number = g(x); //Initial estimate of result

   //Calculate initial gradient
   let fi: number[] = [n];

   //Calculate initial norm
   fi = GradG(x, h);
   // console.log("fi:"+fi);

   //Calculate initial norm
   let DelG: number = 0.0;

   for (let i: number = 0; i < n; ++i) {
       DelG += fi[i] * fi[i];
   }
   DelG = Math.sqrt(DelG);
   let b: number = alpha / DelG;

   //Iterate until value is <= tolerance limit
   while (DelG > tolerance) {
       //Calculate next value
       for (let i = 0; i < n; ++i) {
           x[i] -= b * fi[i];
       }
       h /= 2;

       //Calculate next gradient
       fi = GradG(x, h);
       //Calculate next norm
       DelG = 0;
       for (let i: number = 0; i < n; ++i) {
           DelG += fi[i] * fi[i];
       }

       DelG = Math.sqrt(DelG);
       b = alpha / DelG;

       //Calculate next value
       let g1: number = g(x);

       //Adjust parameter
       if (g1 > g0) alpha /= 2;
       else g0 = g1;
   }

}

// Provides a rough calculation of gradient g(x). export const GradG = (x: number[], h: number) => {

   let n: number = x.length;
   let z: number[] = [n];
   let y: number[] = x;
   let g0: number = g(x);

   // console.log("y:" + y);

   for (let i = 0; i < n; ++i) {
       y[i] += h;
       z[i] = (g(y) - g0) / h;
   }
   // console.log("z:"+z);
   return z;

}

// Method to provide function g(x). export const g = (x: number[]) => {

   return (x[0] - 1) * (x[0] - 1)
       * Math.exp(-x[1] * x[1]) + x[1] * (x[1] + 2)
       * Math.exp(-2 * x[0] * x[0]);

}

export const gradientDescentMain = () => {

   let tolerance: number = 0.0000006;
   let alpha: number = 0.1;
   let x: number[] = [2];

   //Initial guesses
   x[0] = 0.1;
   //of location of minimums 
   x[1] = -1;
   steepestDescent(x, alpha, tolerance);

   console.log("Testing steepest descent method");
   console.log("The minimum is at x[0] = " + x[0]
       + ", x[1] = " + x[1]);
   // console.log("");

}

gradientDescentMain();

</lang>

Output:

Testing steepest descent method
The minimum is at x[0] = 0.10768224291553158, x[1] = -1.2233090211217854