Client Account:   Login
Home Site Statistics   Contact   About Us   Wednesday, April 26, 2017

users on-line: 2 | Forum entries: 6   
Pj0182295- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Optimization Algorithms › ~ Multi-Newton Method

"Optimization Solution"
Multi-Newton Optimization Method
Minimum =
      Value =

f(x,y) = 1.5 (x - 0.5)2 + 3.4(y + 1.2)2 + 2.5
Initial-Array = { , }
[ Tolerance: 1.0e-5]

Multi-Newton Method Optimization

We showed optimization methods applicable to functions with a single variable (i.e functions are defined in one-dimensional space). The Newton-Multi optimization method extends this concept to find the minimum of a function with multiple variables.

Algorithm Creation

The basic idea is simple:

  • Start with an initial array, which represents initial points in n-dimensional space.

  • For each variable, i.e xn, minimize the multi-variable function f(x), where x is a n-dimensional vector.

  • Loop over all the variables.

The minimization along a line with a single variable can be accomplished with one-dimensional optimization algorithm. We applied the Newton optimization.

Testing the Multi-Newton Method

To test it out, we find the minimum of a function with multiple variables, given by:

f(x,y) = 1.5 (x - 0.5)2 + 3.4(y + 1.2)2 + 2.5

           static void TestMultiNewton();
                 double result = Optimization.multiNewton(f1, xarray, 1.0e-5);
                 ListBox1.Items.Add("x = " + result.ToString());
                 ListBox2.Items.Add("f1(x) = " + f1(result).ToString());

To test the Multi-Newton method, we used the function defined above. The user can manipulate initial-array as desired.

Other Implementations...

Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation

Skip Navigation Links.


Home Math, Analysis & More,
  our established expertise..."

  Eigen Inverse Iteration
  Rayleigh-Quotient Method

  Cubic Spline Method
  Newton Divided Difference


Applied Mathematical Algorithms

    Home Complex Functions
A complex number z = x + iy, where...
     Home Non-Linear Systems
Non-linear system methods...
     Home Numerical Differentiation
Construction of numerical differentiation...
     Home Numerical Integration
Consider the function I = ah f(x)dx where...

2006-2017 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |