Solving unconstrained optimization with a new type of conjugate gradient method

Conjugate gradient (CG) methods have been widely used as schemes to solve large-scale unconstrained optimization problems. Numerous studies and modifications have been done recently to improve this method. In this paper, we proposed a new type of CG coefficients (βk) by modification of Polak and Ribiere (PR) method. This new βk is shown to possess global convergence properties by using exact line searches. Performance comparisons are made with the four most common βk proposed by the early researches. Numerical results also show that this new βk performed better.