Robust Conjugate Gradient Methods for Non-smooth Convex Optimization and Image Processing Problems

In order to make the conjugate gradient method more effective and efficient for solving non-smooth optimization problems that have practical significance, various adjustments to the existing Dai-Liao family of conjugate gradient methods have been explored. These modifications are based on the Moreau-Yosida regularization approach and result in search directions that conform to the sufficient descent property and are confined to a suitable trust region. These adapted methods have been proven to have global convergence with mild assumptions and have been tested on both standard test problems and real-world engineering problems such as image processing. The numerical findings suggest that the proposed approaches are efficient and surpass some existing algorithms in the realm of non-smooth optimization. The findings in this chapter will be of great interest to researchers and practitioners working in the fields of optimization and image processing.