Program in C : Digital & Combinatorial Optimization Methods

The following 4 functions are defined : f(x,y)=(x-y)²+x⁴+y⁴ g(x,y)=4x³-24x.y²-48x+3y⁴ h(x,y,z)=xy+xz+yz-x-y-z i(x,y)=(x-y)²+x³+y³ X_number -> X with number below ( i don't know how to write it here) Choose only one of these 4 applications and implement, starting from the initial point of coordinates X_0 = (10,10), in order, the following methods : - Simple Gradient Method (fixed step of value 1/4) - Optimal Step Gradient Method - Conjugate Gradient Method (also known as Fletcher Reeves method) - Polak-Ribière method What I want done : 1. By hand, detail how you get the X_1 iteration on a text file (odt preferred) 2. Then send me the source code in C and the executable that allows the choice of the starting point (so I can change it easily), the step (in the case of a fixed step) and/or any other iteration that you think is relevant. The source code must be easy to understand by anyone who possess C basic notions, commented, not complex functions used. If possible, can be executed on Linux and Windows. Deadline: 1st October