A new structured spectral conjugate gradient method for nonlinear least squares problems

Least squares models appear frequently in many fields, such as data fitting, signal processing, machine learning, and especially artificial intelligence. Nowadays, the model is a popular and sophisticated way to make predictions about real-world problems. Meanwhile, conjugate gradient methods are traditionally known as efficient tools to solve unconstrained optimization problems, especially in high-dimensional cases. This paper presents a new structured spectral conjugate gradient method based on a modification of the modified structured secant equation of Zhang, Xue, and Zhang. The proposed method uses a novel appropriate spectral parameter. It is proved that the new direction satisfies the sufficient descent condition regardless of the line search. The global convergence of the proposed method is demonstrated under some standard assumptions. Numerical experiments show that our proposed method is efficient and can compete with other existing algorithms in this area.