Geometric Representation of Method of Lagrange Multipliers
Geometric Representation of Method of Lagrange Multipliers
This Demonstration gives a geometric representation of the method of Lagrange multipliers. The initial view shows the red point iteratively moving toward a minimum of a specified function. At each iteration, the point takes a small step in the direction, shown by the red arrow, that causes the greatest reduction in the value of the function, i.e. the direction of steepest descent. This direction varies from point to point and can be visualized by the "field" of blue streamlines.
Next, consider what will happen if the point is constrained to move along the circumference of a fixed circle. Check the box labeled "Constrain to circle" to find out. You can explore numerous ways of interacting with this figure, or read the Details section for further information on the method of Lagrange multipliers.