Serial staging with single rocket engine design

Core of the design is an algorithm that accepts as input the following: current payload, the ΔV for the current trip sequence, and a list of ε to use for each stage, and a list of Isp's to use for each stage, and of course, the number of stages to design for. It returns the amount of fuel (mp) and the ms to use for each stage distributed such that this total is the most optimal (minimum) possible for the whole rocket.
The above algorithm is based on optimization theory using Lagrange multiplier as described in the book Orbital Mechanics by Prussing and Conway.

The above algorithm is based on optimization theory using Lagrange multiplier as described in the book Orbital Mechanics by Prussing and Conway.