boxOptimizationjs

• The complex M.J.Box algorithm translated from Fortran 77.
• Autor: Velislav S. Karastoychev.
• email:exel_mmm@abv.bg.
• Date: 5-Aug-2016.
• Description: Finding the minimum of a given multivariable function under double constraints
• Purpose: this program uses the complex method of M.J.Box and is initialy created by Joel A. Richardson and J.L. Kuester in Fortran 77.To use the program, the user must provide the specifical functions jfunc and jconst1,which describe the objective function and the constraints.An example how to use the program is the follow.
• the minimized function
  function jfunc(i,n,m,k,l,x){
  var f = (9 - Math.pow(x[i][0] - 3,2))Math.pow(x[i][1],3)/(27Math.sqrt(3));
  return f;
  }
• the constranits:
  function jconst1(n,m,k,x,i,l){
  var g = new Array(),h = new Array();
  x[i][2] = x[i][0] + Math.sqrt(3)*x[i][1];
  g[0] = 0.0;
  g[1] = 0.0;
  g[2] = 0;
  h[0] = 100;
  h[1] = x[i][0]/Math.sqrt(3);
  h[2] = 6;
  return {g:g,h:h,chi:x};
  }
• the parameters:
  var x = [],alpha = 1.3,beta = 0.001,gamma = 5,delta = 0.0001,
  itmax = 100,n = 2,m = 3,l = 3,k = 4;
  for(i = 0;i < k;i++){
  x[i] = [];
  for(j = 0;j < l;j++){
  x[i][j] = i === 0 && j === 0?1:
  i === 0 && j === 1?0.5:
  i === 0 && j === 2?x[0][0] + Math.sqrt(3)*x[0][1]:0;
  }
  }
• executing:
  programming.Box(n,m,l,k,x,alpha,beta,gamma,delta,itmax,jconst1,jfunc);
  output:=> { x: [ 3.0003939306264016, 1.731787690628987, 5.99993819871818 ],fmin: 0.9995443200842825,iterations: 90 }