Problem 01: Minimization of a Single-variable function using golden section method

Problem Statement: Implement a generic computer program that executes the golden section method. Apply to the following function till the interval is less than 0.001. Provide your computer code, plot optimization history, plot iterative solutions on the function graph, the convergent solution, and describe your observations. For f(x)=2 − 4x + e^x  , carry out a single-variable search using the golden section method to minimize the function. 

Solution: Find the MATLAB code here, code is explained in the comment

Problem 02: Minimization of a multi-variable function using Steepest Descent Method

Problem Statement: Develop a generic computer program that implements the Steepest Descent method. Apply to the following problem. Determine an appropriate termination criterion for this problem. Provide your computer code, a plot of optimization history, iterative solutions on the function graph, the convergent solution, and your observations. You may use either symbolic or numerical differentiation for gradient calculation. Solve

f(x1,x2,x3) = (x1+3*x2+x3)^2 + 4*(x1 - x2 )^2

by using the Steepest Descent method with starting point (-1, 0, 1).

Solution: Find the MATLAB Code here, Code is explained in the comment section

Problem 03: Minimization of a multi-variable function using Fletcher-Reeves Method

Problem Statement: Develop the computer program for implementing the Fletcher-Reeves Conjugate Gradient method for Q2 and compare the algorithm performance (converged solutions, number of iterations) with the Steepest Descent method. 

Solution: Find the MATLAB Code here, Code is explained in the comment section