Home Site Statistics  |   Contact  |   About Us       Thursday, July 29, 2021   

j0182018 - Back to Home

Skip Navigation Links.

   Skip Navigation LinksHOME ›  AREAS OF EXPERTISE ›   Optimization Methods ›  ~ Newton Method

"Optimization Solution"
Newton Optimization Method
Minimum =
      Value =

f(x) = 1.6 x3 + 3x2 - 2x
Initial Value =
[ Tolerance: 1.0e-5]

Newton Method Optimization

It is also possible to use the Newton's root seeking method to find the minimum, maximum, or saddle point of a function, because the derivative of the targeted function is zero at these points.

In this method, the minimum is not bracketed and only one 1 initial guess value of the solution is needed to get the iterative process started to find the minimum of a linear function.

Algorithm Creation

The Newton method uses the following iteration relation:

xn+1 = xn - f'(xn) / f''(xn)

where f'(x) and f''(x) are the first and second derivatives of a function f(x).

Testing the Newton Method

We use the Newton method to find the minimum of a nonlinear function. To test it out, we find the minimum of the same function used to test the Bisection method. Supporting code and methods are not shown.

           static void TestNewton();
                 double result = Optimization.Newton(f, t1, 1.0e-5);
                 ListBox1.Items.Add("x = " + result.ToString());
                 ListBox2.Items.Add("f(x) = " + f(result).ToString());

To test the Newton method, we find the minimum of the same nonlinear function f(x)=1.6x3+3x2-2x used in the Bisection method (see Bisection Method). The user can manipulate initial values 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

Consulting Services - Back to Home

Home Math, Analysis,

Eigen Inverse Iteration
Rayleigh-Quotient Method
Cubic Spline Method


Applied Mathematical Algorithms

Home A complex number z = x + iy, where...

Complex Functions
Home Non-linear system methods...

Non Linear Systems
Home Construction of differentiation...

Home Consider the function where...

About Us

KMP Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.

Contact Us

2461 E Orangethorpe Ave Fullerton, CA 92631 USA info@keystoneminingpost.com
Site Map

   Areas of Expertise
   Reference Items
   Managed Services

Mining & Software Engineering

Since 2006 All Rights Reserved  © KMP Engineering LINKS | PRIVACY POLICY | LEGAL NOTICE