optimization project -- 2

This project requires integrating several existing programs in order to create a program that fundamentally finds an optimal solution to the optimization problem, calculates the Hessian matrix of the second order conditions, and checks whether the Hessian is positive definite, negative definite, indefinite, non-positive definite, or undefined. In this project, this will be done in the first stage for the problem of multi-variable non-constrained optimization, and in the second stage for the problem of multi-variable optimization with equality constraints. In the first stage, the steepest_golden7.c program should be taken, the code for the double nominal rule should be integrated to approximate the Hessian matrix of the Hessian F(x), and the majority of the code from the definite_test1.c program should be run on it. In the second stage, the constr_unit_circle7.c program should be taken and integrated with the majority of the code from the subspace2.c program and the compute_delta() function, along with code that calculates the nominal approximation of the Hessian matrix F(x) + λH(x). The required minimum is found by finding the root of the system of equations obtained by finding the minimum of the sum of the squares of the equations. There is a difficult problem of obtaining high accuracy in these algorithms. It seems that the smallest value of some of the epsilons is 0.003. If the algorithm does not converge to this accuracy, it is possible to reduce the value of epsilon, but the accuracy of the algorithm will be lower.