A new conjugate gradient algorithm for solving large scale unconstrained optimization problems and its applications

Conjugate gradient algorithms are among the primary algorithms used to solve large-scale nonlinear optimization problems. This is due to their advantageous properties, such as no need to compute second-order derivatives when calculating algorithmic steps, low storage requirements, rapid results, and global convergence. Conjugate gradient algorithms are utilized in areas such as industry, engineering optimization problems, neural network training, and image restoration. In this thesis, a new conjugate gradient algorithm is introduced, and it is shown that this algorithm strongly converges to the solution of the minimization problem and satisfies the sufficient descent property when used with Armijo and Wolfe line search techniques. Finally, a performance profile comparison of the algorithm is presented, along with its application to the image restoration problem.