Elements of Numerical Mathematical Economics with Excel

9.2. Discrete approximate Calculus of Variations: Lagrange multipliers and contour lines solutions

We have now all the essential necessary elements to solve our CoV problem in a discrete numerical manner without passing through the Euler–Lagrange equation.

First approach to solve the Calculus of Variations in a numerical framework: Lagrange multipliers

Let us propose the following general discretization of the simplest problem 9.1-2 :

maximize or minimize J d i s c r e t e = ∑ i = 1 n F i [ ( y 0 + ∑ k = 1 i Δ k y ) , ( Δ i y ) ( Δ i t ) , t i ] Δ i t

(9.2-1)

s . t . ∑ i = 1